On graph products of spaces, groups and Hopf algebras
On graph products of spaces, groups and Hopf algebras
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Li Cai, Xi鈥檃n Jiaotong-Liverpool University
Online Talk
In this talk we show that, the loop space X of a graph product of spaces is given by听(up to weak homotopy equivalence of topological monoids) a graph product of simplicial groups,听using Kan鈥檚 construction of loop spaces on simplicial sets. As a consequence, we obtain a theorem听of Dobrinskaya: when X is connected, its homology (with coefficients from a field) is a graph product听H of connected Hopf algebras. Some properties of the commutator of H will also be discussed.
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