WI-posets, graph complexes and Z_2-equivalences

Details WI-posets, graph complexes and Z_2-equivalences WI-posets, graph complexes and Z_2-equivalences

2004-05-21

arxiv.org/abs/math/0405419v1

Mathematics

Combinatorics

Scientific paper

We introduce WI-posets as intermediate objects in the study of Z_2-homotopy types of graph complexes. It turns out that (almost) all graph complexes associated to a graph can be viewed as avatars of the same object, as long as their Z_2-homotopy types are concerned. Among the applications are a proof that each finite, free Z_2-complex is a graph complex and an evaluation of Z_2-homotopy types of complexes Ind(C_n) of independence sets in a cycle C_n. The main tools used in the paper are Quillen fiber theorem and Bredon criterion for Z_2-equivalence of Z_2-complexes.

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