Mapping class groupoids and Thompson's groups

Abstract

We introduce a groupoid ${\mathbf{Î MG}}}$, called the fundamental modular groupoid, which is a variant of Penner's mapping class groupoid. We study how it relates to the surface mapping class groups and Thompson's group $\mathsf{T}$. We also introduce larger groupoid $\hat{\mathbf{I}}\text{c◯}\mathbf{MG}$, which is related to outer automorphisms of free groups and Thompson's group $\mathsf{V}$ in a similar manner.

43 pages, 24 figures