268
268

Jan 11, 2022
01/22

by
Munkres, James R., 1930-

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xvi, 537 pages : 25 cm

Topics: Topology, Algebraic topology

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11

Mar 14, 2022
03/22

by
Longueville, Mark de

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xi, 238 p. : 24 cm

Topics: Combinatorial topology, Topology

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6.0

Jun 29, 2018
06/18

by
Vesko Valov

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The homological dimension $d_G$ of metric compacta was introduced by Alexandroff. In this paper we provide some general properties of $d_G$, mainly with an eye towards describing the dimensional full-valuedness of compact metric spaces. As a corollary of the established properties of $d_G$, we prove that any two-dimensional $lc^2$ metric compactum is dimensionally full-valued. This improves the well known result of Kodama that every two-dimensional $ANR$ is dimensionally full-valued....

Topics: General Topology, Geometric Topology, Algebraic Topology, Mathematics

Source: http://arxiv.org/abs/1605.04497

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4.0

Jun 30, 2018
06/18

by
Matija Cencelj; Umed H. Karimov; Dušan D. Repovš

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We investigate the classical Alexandroff-Borsuk problem in the category of non-triangulable manifolds: Given an $n$-dimensional compact non-triangulable manifold $M^n$ and $\varepsilon > 0$, does there exist an $\varepsilon$-map of $M^n$ onto an $n$-dimensional finite polyhedron which induces a homotopy equivalence?

Topics: Algebraic Topology, General Topology, Geometric Topology, Mathematics

Source: http://arxiv.org/abs/1703.01057

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5.0

Jun 30, 2018
06/18

by
Leonard R. Rubin; Vera Tonić

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In extension theory, in particular in dimension theory, it is frequently useful to represent a given compact metrizable space X as the limit of an inverse sequence of compact polyhedra. We are going to show that, for the purposes of extension theory, it is possible to replace such an X by a better metrizable compactum Z. This Z will come as the limit of an inverse sequence of triangulated polyhedra with simplicial bonding maps that factor in a certain way. There will be a cell-like map from Z...

Topics: Algebraic Topology, General Topology, Geometric Topology, Mathematics

Source: http://arxiv.org/abs/1703.04339

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6.0

Jun 29, 2018
06/18

by
Fredric D. Ancel; Robert D. Edwards

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This paper presents some partial answers to the following question. QUESTION. If a normal space X is the union of an increasing sequence of open sets U(1), U(2), U(3) ... such that each U(n) contracts to a point in X, must X be contractible? The main results of the paper are: THEOREM 1. If a normal space X is the union of a sequence of open subsets { U(n) } such that the closure of U(n) is contained in U(n+1) and U(n) contracts to a point in U(n+1) for each n > 0, then X is contractible....

Topics: General Topology, Geometric Topology, Algebraic Topology, Mathematics

Source: http://arxiv.org/abs/1606.05379

Due to the rapid growth of the Internet, the available pool of unique addresses in version four of the Internet Protocol (IPv4) is nearly depleted. As a result, the next generation protocol, IPv6, is now widely implemented and rapidly being adopted. This thesis examines new methods for active mapping of the IPv6 topology, i.e., router and link discovery. Better characterization of the IPv6 topology can provide the Department of Defense and other federal agencies the ability to defend networks...

Topics: Internet Topology, Network Topology, IPv6, IPv6 Topology, Adaptive Probing, Efficient Topology...

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8.0

Nov 9, 2022
11/22

by
Yan, Min, 1964-

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1 online resource

Topics: Topology -- Textbooks, Point set theory -- Textbooks, Algebraic topology -- Textbooks, MATHEMATICS...

5
5.0

Jun 30, 2018
06/18

by
Jonathan Ariel Barmak; Elias Gabriel Minian

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We describe the second homotopy group of any CW-complex $K$ by analyzing the universal cover of a locally finite model of $K$ using the notion of $G$-coloring of a partially ordered set. As applications we prove a generalization of the Hurewicz theorem, which relates the homotopy and homology of non-necessarily simply-connected complexes, and derive new results on asphericity for two-dimensional complexes and group presentations.

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1412.4835

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44

Jul 2, 2019
07/19

by
Singer, I. M

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232 pages ; 24 cm

Topics: Algebraic topology, Geometry, Differential, Topology

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3.0

Jun 30, 2018
06/18

by
A. Cattabriga; T. Nasybullov

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We construct a virtual quandle for links in lens spaces $L(p,q)$, with $q=1$. This invariant has two valuable advantages over an ordinary fundamental quandle for links in lens spaces: the virtual quandle is an essential invariant and the presentation of the virtual quandle can be easily written from the band diagram of a link.

Topics: Algebraic Topology, Geometric Topology, Mathematics

Source: http://arxiv.org/abs/1702.05964

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Jun 30, 2018
06/18

by
Sergey A. Antonyan

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In his seminal work \cite{pal:61}, R. Palais extended a substantial part of the theory of compact transformation groups to the case of proper actions of locally compact groups. Here we extend to proper actions some other important results well known for compact group actions. In particular, we prove that if $H$ is a compact subgroup of a locally compact group $G$ and $S$ is a small (in the sense of Palais) $H$-slice in a proper $G$-space, then the action map $G\times S\to G(S)$ is open. This is...

Topics: General Topology, Geometric Topology, Mathematics

Source: http://arxiv.org/abs/1702.08093

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10.0

Jun 29, 2018
06/18

by
Vesko Valov

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There are different definitions of homological dimension of metric compacta involving either \v{C}ech homology or exact (Steenrod) homology. In this paper we investigate the relation between these homological dimensions with respect to different groups. It is shown that all homological dimensions of a metric compactum X with respect to any field coincide provided X is homologically locally connected with respect to the singular homology up to dimension n=dim X. We also prove that any...

Topics: General Topology, Geometric Topology, Mathematics

Source: http://arxiv.org/abs/1611.08347

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Jun 26, 2018
06/18

by
Kyle Evans-Lee; Nikolai Saveliev

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The configuration space $F_2 (M)$ of ordered pairs of distinct points in a manifold $M$, also known as the deleted square of $M$, is not a homotopy invariant of $M$: Longoni and Salvatore produced examples of homotopy equivalent lens spaces $M$ and $N$ of dimension three for which $F_2 (M)$ and $F_2 (N)$ are not homotopy equivalent. In this paper, we study the natural question whether two arbitrary $3$-dimensional lens spaces $M$ and $N$ must be homeomorphic in order for $F_2 (M)$ and $F_2 (N)$...

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1502.03408

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Jun 28, 2018
06/18

by
Matthias Kreck; Haggai Tene

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In this paper we use tools from differential topology to give a geometric description of cohomology for Hilbert manifolds. Our model is Quillen's geometric description of cobordism groups for finite dimensional smooth manifolds \cite{Q}. Quillen stresses the fact that this construction allows the definition of Gysin maps for "oriented" proper maps. For finite dimensional manifolds one has a Gysin map in singular cohomology which is based on Poincar\'e duality, hence it is not clear...

Topics: Algebraic Topology, Mathematics, Geometric Topology

Source: http://arxiv.org/abs/1506.07075

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Jun 30, 2018
06/18

by
Soren Galatius; Oscar Randal-Williams

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We prove a homological stability theorem for moduli spaces of simply-connected manifolds of dimension $2n > 4$, with respect to forming connected sum with $S^n \times S^n$. This is analogous to Harer's stability theorem for the homology of mapping class groups. Combined with previous work of the authors, it gives a calculation of the homology of the moduli spaces of manifolds diffeomorphic to connected sums of $S^n \times S^n$ in a range of degrees.

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1403.2334

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5.0

Jun 30, 2018
06/18

by
Piotr Beben; Stephen Theriault

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We determine loop space decompositions of simply-connected four-manifolds, $(n-1)$-connected $2n$-dimensional manifolds provided $n\notin\{4,8\}$, and connected sums of products of two spheres. These are obtained as special cases of a more general loop space decomposition of certain torsion-free $CW$-complexes with well-behaved skeleta and some Poincar\'{e} duality features.

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1406.0651

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Jun 30, 2018
06/18

by
Kei Irie

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The aim of this paper is to define a chain level refinement of the Batalin-Vilkovisky (BV) algebra structure on the homology of the free loop space of a closed, oriented $C^\infty$-manifold. For this purpose, we define a (nonsymmetric) cyclic dg operad which consists of "de Rham chains" of free loops with marked points. A notion of de Rham chains, which is a certain hybrid of the notions of singular chains and differential forms, is a key ingredient in our construction. Combined with...

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1404.0153

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9.0

Jun 29, 2018
06/18

by
Benson Farb; Jesse Wolfson; Melanie Matchett Wood

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Motivated by analogies with basic density theorems in analytic number theory, we introduce a notion (and variations) of the {\em homological density} of one space in another. We use Weil's number field/ function field analogy to predict coincidences for limiting homological densities of various sequences $\mathcal{Z}^{(d_1,\ldots,d_m)}_n(X)$ of spaces of $0$-cycles on manifolds $X$. The main theorem in this paper is that these topological predictions, which seem strange from a purely...

Topics: Geometric Topology, Algebraic Topology, Mathematics

Source: http://arxiv.org/abs/1611.04563

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6.0

Jun 30, 2018
06/18

by
James J. Walton

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This thesis establishes a generalised setting with which to unify the study of finite local complexity (FLC) patterns. The abstract notion of a "pattern" is introduced, which may be seen as an analogue of the space group of isometries preserving a tiling but where, instead, one considers partial isometries preserving portions of it. These inverse semigroups of partial transformations are the suitable analogue of the space group for patterns with FLC but few global symmetries. In a...

Topics: Mathematics, General Topology, Algebraic Topology

Source: http://arxiv.org/abs/1405.6134

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Jun 28, 2018
06/18

by
Dan Jones; Andrew Lobb; Dirk Schuetz

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We pursue the analogy of a framed flow category with the flow data of a Morse function. In classical Morse theory, Morse functions can sometimes be locally altered and simplified by the Morse moves. These moves include the Whitney trick which removes two oppositely framed flowlines between critical points of adjacent index and handle cancellation which removes two critical points connected by a single flowline. A framed flow category is a way of encoding flow data such as that which may arise...

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1507.03502

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7.0

Jun 30, 2018
06/18

by
Keiichi Sakai

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In this paper we study the Haefliger invariant for long embeddings $\mathbb{R}^{4k-1}\hookrightarrow\mathbb{R}^{6k}$ in terms of the self-intersections of their projections to $\mathbb{R}^{6k-1}$, under the condition that the projection is a generic long immersion $\mathbb{R}^{4k-1}\looparrowright\mathbb{R}^{6k-1}$. We define the notion of "crossing changes" of the embeddings at the self-intersections and describe the change of the isotopy classes under crossing changes using the...

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1405.1947

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11

Nov 8, 2022
11/22

by
Murdeshwar, M. G

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viii, 369 p. : 25 cm

Topic: Topology

430
430

Aug 31, 2019
08/19

by
Croom, Fred H., 1941-

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xi, 312 p. : 24 cm

Topic: Topology

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94

Jan 11, 2021
01/21

by
Christenson, Charles O

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xi, 517 p. : 24 cm

Topic: Topology

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0.0

Nov 23, 2022
11/22

by
Eilenberg, Samuel

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xv, 328 p. 24 cm

Topic: Topology

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40

Jul 17, 2019
07/19

by
Aleksandrov, P. S. (Pavel Sergeevich), 1896-

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98

Jun 26, 2019
06/19

by
Császár, Ákos

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488 p. ; 25 cm

Topic: Topology

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16

Apr 25, 2022
04/22

by
Vasilʹev, V. A., 1956-

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xiii, 149 p. : 22 cm

Topic: Topology

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442

Jul 24, 2019
07/19

by
Steenrod, Norman Earl, 1910-1971

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vii, 224 p. 24 cm

Topic: Topology

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52

Aug 31, 2019
08/19

by
Hu, S. T. (Sze-Tsen), 1914-

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x, 214 p. 24 cm

Topic: Topology

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60

Oct 17, 2021
10/21

by
Eisenberg, Murray, 1939-

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xiv, 427 p. 25 cm

Topic: Topology

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64

Jan 28, 2019
01/19

by
Čech, Eduard, 1893-1960

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893 p. ; 25 cm

Topic: Topology

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38

Jul 20, 2022
07/22

by
Willard, Stephen, 1941-

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xii, 369 p. : 24 cm

Topic: Topology

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IV, 251 Seiten

Topic: Topology

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27

Jul 17, 2019
07/19

by
Nagata, Jun-iti, 1925-

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x, 365 p. ; 23 cm

Topic: Topology

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36

Jul 30, 2019
07/19

by
Lefschetz, Solomon, 1884-

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vi, 389 p. ; 26 cm

Topic: Topology

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19

Sep 12, 2022
09/22

by
Chinn, William G

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viii, 160 p. 23 cm

Topic: Topology

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123

Dec 4, 2009
12/09

by
Hurewicz, Witold, 1904-1956; Wallman, Henry, 1915- joint author

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4.0

Jun 30, 2018
06/18

by
Julien Korinman

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We state a simple criterion to prove the infiniteness of the image of Reshetikhin-Turaev representations of the mapping class groups of surfaces at odd prime levels. We use it to study some of the Reshetikhin-Turaev representations associated to the one-holed torus and derive an alternative proof of a result of Funar.

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1412.2671

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Jun 30, 2018
06/18

by
Jozef H. Przytycki

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This paper is a sequel to my essay "Distributivity versus associativity in the homology theory of algebraic structures" Demonstratio Math., 44(4), 2011, 821-867 (arXiv:1109.4850 [math.GT]). We start from naive invariants of arc colorings and survey associative and distributive magmas and their homology with relation to knot theory. We outline potential relations to Khovanov homology and categorification, via Yang-Baxter operators. We use here the fact that Yang-Baxter equation can be...

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1409.7044

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5.0

Jun 30, 2018
06/18

by
John R. Parker; Li-Jie Sun

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In this paper we will consider the 2-fold symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2pi/p with p no smaller than 2. We will mainly concentrate on the groups where some elements are elliptic of finite order. Then we will classify all such groups which are candidates for being discrete. There are only 4 types.

Topics: Algebraic Topology, Geometric Topology, Mathematics

Source: http://arxiv.org/abs/1702.04888

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Jun 28, 2018
06/18

by
D. Kotschick; C. Loeh; C. Neofytidis

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We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1507.01413

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7.0

Jun 30, 2018
06/18

by
Qayum Khan

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Let $n$ be a positive integer, and let $\ell>1$ be square-free odd. We classify the set of equivariant homeomorphism classes of free $C_\ell$-actions on the product $S^1 \times S^n$ of spheres, up to indeterminacy bounded in $\ell$. The description is expressed in terms of number theory. The techniques are various applications of surgery theory and homotopy theory, and we perform a careful study of $h$-cobordisms. The $\ell=2$ case was completed by B Jahren and S Kwasik (2011). The new...

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1405.0699

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5.0

Jun 30, 2018
06/18

by
Ricardo Garcia Lopez

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Given a finite simplicial complex, a unimodular representation of its fundamental group and a closed twisted cochain of odd degree, we define a twisted version of the Reidemeister torsion, extending a previous definition of V. Mathai and S. Wu. The main tool is a complex of piecewise smooth currents, defined by J. Dupont.

Topics: Mathematics, Algebraic Topology, Geometric Topology

Source: http://arxiv.org/abs/1407.0301

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Jun 28, 2018
06/18

by
Yadira Barreto; Santiago López de Medrano; Alberto Verjovsky

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We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restric- tions. II. We also show, using a recent deep result about contact forms due to Borman, Eliashberg and Murphy [6], that every odd-dimensional moment-angle manifold admits a contact structure. This contrasts with the fact that, except for a few, well-determined cases, even-dimensional ones do not admit symplectic structures. We obtain the same results for...

Topics: Algebraic Topology, Mathematics, Geometric Topology

Source: http://arxiv.org/abs/1510.07729

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5.0

Jun 28, 2018
06/18

by
Konrad Królicki; Paweł Krupski

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The family of Wilder continua in cubes of dimension > 2 and its two subfamilies-of continuum-wise Wilder continua and of hereditarily arcwise connected continua-are recognized as coanalytic absorbers in the hyperspace of subcontinua of the cubes. In particular, each of them is homeomorphic to the set of all nonempty countable closed subsets of the unit interval.

Topics: Geometric Topology, General Topology, Mathematics

Source: http://arxiv.org/abs/1512.05802

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4.0

Jun 28, 2018
06/18

by
Oleg R. Musin

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We prove that if the circle group acts smooth and unitary on 2n-dimensional stably complex manifold with two isolated fixed points and it is not bound equivariantly, then n=1 or 3. Our proof relies on the rigid Hirzebruch genera.

Topics: Algebraic Topology, Mathematics, Geometric Topology

Source: http://arxiv.org/abs/1512.03528

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Jun 30, 2018
06/18

by
Margarita Toro; Mauricio Rivera

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We introduce the Schubert form a $3$-bridge link diagram, as a generalization of the Schubert normal form of a $3$-bridge link. It consists of a set of six positive integers, written as $\left( p/n,q/m,s/l\right) $, with some conditions and it is based on the concept of $3$-butterfly. Using the Schubert normal form of a $3$-bridge link diagram, we give two presentations of the 3-bridge link group. These presentations are given by concrete formulas that depend on the integers $\left\{...

Topics: Algebraic Topology, Geometric Topology, Mathematics

Source: http://arxiv.org/abs/1703.00041