On graph products of spaces, groups and Hopf algebras

Li Cai, Xi’an Jiaotong-Liverpool University

Online Talk

In this talk we show that, the loop space X of a graph product of spaces is given by (up to weak homotopy equivalence of topological monoids) a graph product of simplicial groups, using Kan’s construction of loop spaces on simplicial sets. As a consequence, we obtain a theorem of Dobrinskaya: when X is connected, its homology (with coefficients from a field) is a graph product H of connected Hopf algebras. Some properties of the commutator of H will also be discussed.