WI-posets, graph complexes and Z2-equivalences
Abstract
We introduce WI-posets as intermediate objects in the study of Z2-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 Z2-homotopy types are concerned. Among the applications are a proof that each finite, free Z2-complex is a graph complex and an evaluation of Z2-homotopy types of complexes Ind(Cn) of independence sets in a cycle Cn. The main tools used in the paper are Quillen fiber theorem and Bredon criterion for Z2-equivalence of Z2-complexes.
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