2025/04/16 by Mallika Roy, Roy, Mallika
Mathematics · #Geometric and Algebraic Topology #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2504.12409
A group, whose presentation is explicitly derived in a certain way from a word labelled oriented graph (in short, WLOG), is called a WLOG group. In this work, we study homological version of Bogomolov multiplier (denoted by \widetildeB0) for this family of groups. We prove how to compute the generators for the \widetildeB0(G) of a WLOG group G from the underlying WLOG. We exhibit finitely presented Bestvina--Brady groups and Artin groups as WLOG groups. As applications, we compute both the multipliers: the homological version of Bogomolov multipliers and Schur multipliers, of these groups utilizing their respective WLOG group presentations. Our computation gives a new proof of the structure of the Schur multiplier of a finitely presented Bestvina--Brady group.