On graph products of spaces, groups and Hopf algebras
On graph products of spaces, groups and Hopf algebras

Li Cai, Xi’an JiaotongLiverpool 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.