Geodesic
On the homotopy invariance of configuration spaces
Aouina, Mokhtar1 ; Klein, John R1
1Department of Mathematics, Wayne State University, Detroit MI 48202, USA
Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 813-827
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For a closed PL manifold M, we consider the configuration space F(M,k) of ordered k–tuples of distinct points in M. We show that a suitable iterated suspension of F(M,k) is a homotopy invariant of M. The number of suspensions we require depends on three parameters: the number of points k, the dimension of M and the connectivity of M. Our proof uses a mixture of Poincaré embedding theory and fiberwise algebraic topology.

DOI : 10.2140/agt.2004.4.813
Keywords: configuration space, fiberwise suspension, embedding up to homotopy, Poincaré embedding

Aouina, Mokhtar  1   ; Klein, John R  1

1 Department of Mathematics, Wayne State University, Detroit MI 48202, USA 
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Aouina, Mokhtar; Klein, John R. On the homotopy invariance of configuration spaces. Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 813-827. doi: 10.2140/agt.2004.4.813

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