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Displaying similar documents to “Homotopy type of Euclidean configuration spaces”

Embedding proper homotopy types

M. Cárdenas, T. Fernández, F. F. Lasheras, A. Quintero (2003)

Colloquium Mathematicae

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We show that the proper homotopy type of any properly c-connected locally finite n-dimensional CW-complex is represented by a closed polyhedron in ℝ 2 n - c (Theorem I). The case n - c ≥ 3 is a special case of a general proper homotopy embedding theorem (Theorem II). For n - c ≤ 2 we need some basic properties of “proper” algebraic topology which are summarized in Appendices A and B. The results of this paper are the proper analogues of classical results by Stallings [17] and Wall [20] for finite...

On the homotopy type of Diff ( M n ) and connected problems

Dan Burghelea (1973)

Annales de l'institut Fourier

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This paper reports on some results concerning: a) The homotopy type of the group of diffeomorphisms Diff ( M n ) of a differentiable compact manifold M n (with C ∞ -topology). b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo M n (with C o -topology). As a biproduct, one gets new facts about the homotopy groups of Diff ( D n , ∂ D n ) , Top n , Top n / O n and about the number of connected components of the space of topological and combinatorial pseudoisotopies. ...

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.

Free loop spaces and cyclohedra

Markl, Martin

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It is well-known that a based space is of the weak homotopy type of a loop space iff it is a grouplike algebra over an A ∞ -operad. The classical model for such an operad consists of Stasheff’s associahedra. The present paper describes a similar recognition principle for free loop spaces. Let 𝒫 be an operad, M a 𝒫 -module and U a 𝒫 -algebra. An M -trace over U consists of a space V and a module homomorphism T : M → End U , V over the operad homomorphism 𝒫 → End U given by the algebra structure on U . Let 𝒞 1 be the...

On certain homotopy actions of general linear groups on iterated products

Ran Levi, Stewart Priddy (2001)

Annales de l’institut Fourier

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The n -fold product X n of an arbitrary space usually supports only the obvious permutation action of the symmetric group Σ n . However, if X is a p -complete, homotopy associative, homotopy commutative H -space one can define a homotopy action of GL n ( ℤ p ) on X n . In various cases, e.g. if multiplication by p r is null homotopic then we get a homotopy action of G L n ( ℤ / p r ) for some r . After one suspension this allows one to split X n using idempotents of 𝔽 p GL n ( ℤ / p ) which can be lifted to 𝔽 p GL n ( ℤ / p r ) . In fact all of this is possible...