2020/01/13 by Cihan Okay, Okay, Cihan, Pál Zsámboki +1
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2001.04052
openalex publication_date 2020/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a simplicial analog of classifying spaces for commutativity which classify principal bundles with commutativity structure on their transition functions. Our construction W(τ,K), which takes as input a simplicial group K and a cosimplicial group τ that encodes the additional structure such as commutativity, is a variation of the W-construction for simplicial groups. Our main result shows that the geometric realization of our W(τ,K) is homotopy equivalent to the topological classifying space B(τ,|K|).