2004/05/21 by Rade T. Živaljević, Rade T. Zivaljevic, Zivaljevic, Rade T. · 2 citations
Computer Science · Mathematics · #05C10 #05C15 #06A07 #55P91 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.CO #msc:05C10 #msc:05C15 #msc:06A07 #msc:55P91
paper · pdf · doi:10.48550/arxiv.math/0405419
arxiv created 2004/05/21 · openalex publication_date 2004/05/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.