Work

Commutative classifying space for simplicial groups

Year: 2026

Type: article

Abstract: 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 $$\overline{W}(\tau ,K)$$ W ¯ ( τ , K ) , which takes as input a simplicial group K and a cosimplicial group $$\tau $$ τ that encodes the additional structure such as commutativity, is a variation of the $$\overline{W}$$ W ¯ -construction for simplicial groups. Our main result shows that the geometric realization of our $$\overline{W}(\tau ,K)$$ W ¯ ( τ , K ) is homotopy equivalent to the topological classifying space $$B(\tau ,|K|)$$ B ( τ , | K | ) .

Source: Journal of Homotopy and Related Structures

DOI: 10.1007/s40062-026-00397-w

Authors: Cihan Okay, Pál Zsámboki

Institutions: Bilkent University, HUN-REN Alfréd Rényi Institute of Mathematics

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal