## Topology and Geometry Seminar

Title: Geometric subgroups of the mapping class group

Speaker: Jamil Mortada

Abstract:
My talk is based on a paper by Rolfsen and Paris. I will discuss "geometric" subgroups of the mapping class group. If N is a subsurface of M, then the inclusion map i : N ---> M induces a natural homomorphism
i_{\ast} : Mod(N) ---> Mod(M). The image i_{\ast}(Mod(N)) is called a geometric subgroup of Mod(M). I will determine Ker(i_{\ast}) and give necessary and sufficient conditions for the injectivity of i_{\ast}.