Loops on polyhedral products and diagonal arrangements

Details Loops on polyhedral products and diagonal arrangements Loops on polyhedral products and diagonal arrangements

2009-01-19

arxiv.org/abs/0901.2871v1

Mathematics

Algebraic Topology

32 pages

Scientific paper

In this paper we establish a connection between the loop space homology of the generalization of wedge defined by a simplicial complex K (so called polyhedral product) and the homology of certain diagonal arrangements associated with K. We illustrate these results by finding the presentations of those loop homology algebras for certain K generalizing results of Panov-Ray, Papadima-Suciu, Lemaire. Finally, we show that in the case when the functor is applied to suspensions, this homology splitting comes from the stable homotopy splitting of the loop spaces.

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