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

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 ( ∏ i X i ) with those of ∏ 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.

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 .

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 ← B G ← B Γ 2 . Denote by ξ the diagram I p ← H 1 → X = H , where p is the natural map onto the unit interval. We show that the N i l ∼ 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...

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 → 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.

Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers

Robert Lipshitz, David Treumann (2016)

Journal of the European Mathematical Society

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Let A be a dg algebra over 𝔽 2 and let M be a dg A -bimodule. We show that under certain technical hypotheses on A , a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product M ⊗ A L M and converges to the Hochschild homology of M . We apply this result to bordered Heegaard Floer theory, giving spectral sequences associated to Heegaard Floer homology groups of certain branched and unbranched double covers.

A note on product structures on Hochschild homology of schemes

Abhishek Banerjee (2011)

Colloquium Mathematicae

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We extend the definition of Hochschild and cyclic homologies of a scheme over a commutative ring k to define the Hochschild homologies HH⁎(X/S) and cyclic homologies HC⁎(X/S) of a scheme X with respect to an arbitrary base scheme S. Our main purpose is to study product structures on the Hochschild homology groups HH⁎(X/S). In particular, we show that H H ⁎ ( X / S ) = ⨁ n ∈ ℤ H H ₙ ( X / S ) carries the structure of a graded algebra.

Homological computations in the universal Steenrod algebra

A. Ciampella, L. A. Lomonaco (2004)

Fundamenta Mathematicae

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We study the (bigraded) homology of the universal Steenrod algebra Q over the prime field ₂, and we compute the groups H s , s ( Q ) , s ≥ 0, using some ideas and techniques of Koszul algebras developed by S. Priddy in [5], although we presently do not know whether or not Q is a Koszul algebra. We also provide an explicit formula for the coalgebra structure of the diagonal homology D ⁎ ( Q ) = ⨁ s ≥ 0 H s , s ( Q ) and show that D⁎(Q) is isomorphic to the coalgebra of invariants Γ introduced by W. Singer in [6].