Tyrone Ghaswala, Department of Pure Mathematics, University of Waterloo
"Mapping class groups, coverings, braids and groupoids"
Suppose you are handed a finite sheeted (possibly branched) covering space between closed 2-manifolds by an eccentric mathematician. A natural question to ask is what is the relationship between the mapping class group of the covering surface and the mapping class group of the base surface?
In this talk, we will take a journey through this question for surfaces with boundary. Along the way, we will encounter a appearances from the fundamental groupoid, a classical theorem of Birman and Hilden, and the Burau representation for braid groups.
No familiarity with mapping class groups or eccentric mathematicians will be assumed. This is joint work with Alan McLeay.
MC 5413