Homotopy groups of arc complements in $S^n$ or Q

S. Singh

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Displaying similar documents to “Homotopy groups of arc complements in $S^{n}$ or Q”

On the Hurewicz theorem for wedge sum of spheres.

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Revista Colombiana de Matemáticas

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A note on singular homology groups of infinite products of compacta

Kazuhiro Kawamura (2002)

Fundamenta Mathematicae

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Let n be an integer with n ≥ 2 and $X_{i}$ be an infinite collection of (n-1)-connected continua. We compare the homotopy groups of $Σ (\prod_{i} X_{i})$ with those of $\prod_{i} Σ X_{i}$ (Σ denotes the unreduced suspension) via the Freudenthal Suspension Theorem. An application to homology groups of the countable product of the n(≥ 2)-sphere is given.

Homotopy Invariance of Transverse Homology Functors

Sara Dragotti, Gaetano Magro, Lucio Parlato (2007)

Bollettino dell'Unione Matematica Italiana

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We construct, here, transverse homology functors, and we prove their invariance with respect to a suitable definition of homotopy.

Homology cobordism group of homology 3-spheres.

Mikio Furuta (1990)

Inventiones mathematicae

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Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds

Hajime Sato (1972)

Annales de l'institut Fourier

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We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold $M^{n}$ . The main theorem says that there is a unique obstruction element in $H_{n - 4} (M, ℋ^{3})$ , where $ℋ^{3}$ is the group of 3-dimensional PL-homology spheres modulo those which are the boundary of an acyclic PL-manifold. If the obstruction is zero and $M$ is compact, we obtain a PL-manifold which is simple homotopy equivalent to $M$ .

A Converse to the P.A. Smith Theorem for Nonunitary Homology Spheres.

Reinhard Schultz (1985)

Manuscripta mathematica

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Waldhausen’s Nil groups and continuously controlled K-theory

Hans Munkholm, Stratos Prassidis (1999)

Fundamenta Mathematicae

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Let $Γ = Γ_{1} *_{G} Γ_{2}$ be the pushout of two groups $Γ_{i}$ , i = 1,2, over a common subgroup G, and H be the double mapping cylinder of the corresponding diagram of classifying spaces $B Γ_{1} \leftarrow B G \leftarrow B Γ_{2}$ . Denote by ξ the diagram $I \frac{p}{\leftarrow} H \frac{1}{\to} X = H$ , where p is the natural map onto the unit interval. We show that the $N i l^{\sim}$ groups which occur in Waldhausen’s description of $K_{*} (ℤ Γ)$ coincide with the continuously controlled groups $_{*}^{c c} (ξ)$ , defined by Anderson and Munkholm. This also allows us to identify the continuously controlled groups $_{*}^{c c} (ξ^{+})$ which are known to form...

Combinatorial homology in a perspective of image analysis.

Grandis, Marco (2003)

Georgian Mathematical Journal

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Homology fibrations and “group-completion” revisited.

Pitsch, Wolfgang, Scherer, Jérôme (2004)

Homology, Homotopy and Applications

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Homology and homotopy groups of the complement of certain family of fibers in a critical point problem.

Pintea, Cornel (2005)

Balkan Journal of Geometry and its Applications (BJGA)

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Effective homology for homotopy colimit and cofibrant replacement

Marek Filakovský (2014)

Archivum Mathematicum

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We extend the notion of simplicial set with effective homology presented in [22] to diagrams of simplicial sets. Further, for a given finite diagram of simplicial sets $X : ℐ \to sSet$ such that each simplicial set $X (i)$ has effective homology, we present an algorithm computing the homotopy colimit $hocolim X$ as a simplicial set with effective homology. We also give an algorithm computing the cofibrant replacement $X^{cof}$ of $X$ as a diagram with effective homology. This is applied to computing of equivariant cohomology...

A faithful linear-categorical action of the mapping class group of a surface with boundary

Robert Lipshitz, Peter Ozsváth, Dylan P. Thurston (2013)

Journal of the European Mathematical Society

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We show that the action of the mapping class group on bordered Floer homology in the second to extremal spin $^{c}$ -structure is faithful. This paper is designed partly as an introduction to the subject, and much of it should be readable without a background in Floer homology.

Rational string topology

Yves Félix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2007)

Journal of the European Mathematical Society

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We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold $M$ . We prove that the loop homology of $M$ is isomorphic to the Hochschild cohomology of the cochain algebra $C^{*} (M)$ with coefficients in $C^{*} (M)$ . Some explicit computations of the loop product and the string bracket are given.

Displaying similar documents to “Homotopy groups of arc complements in S n or Q”

Displaying similar documents to “Homotopy groups of arc complements in $S^{n}$ or Q”