WI-posets, graph complexes and Z_2-equivalences
Combinatorics
2007-05-23 v1 Algebraic Topology
Abstract
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.
Keywords
Cite
@article{arxiv.math/0405419,
title = {WI-posets, graph complexes and Z_2-equivalences},
author = {Rade T. Zivaljevic},
journal= {arXiv preprint arXiv:math/0405419},
year = {2007}
}