3:30 pm, Seminar Hall
Introduction to Mapping Class Groups
Kashyap Rajeevsarathy
IISER, Bhopal.
19-03-19

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Abstract

Let $S_{g,b,p}$ denote the closed orientable surface of genus $g$ with $b$ boundary components, and $p$ punctures. The \textit{mapping class group} of $S = S_{g,b,p}$ (denoted by $\text{Mod}(S)$) is defined to be the group of isotopy classes of orientation preserving self-homeomorphisms of $S$ that restrict to the identity on $\partial S$ and preserve the set of punctures in $S$. In this two-part lecture series, we will introduce various concepts and ideas that lie at the foundation of the theory of mapping class groups. We will also explore some of its connections with hyperbolic geometry, Braid groups, Teichm\"{u}ller theory, and $3$-manifolds.