Mapping Class Groups of Sliced Loch Ness Monsters by Ryan Dickmann

Geometry Topology Seminar
Monday, August 22, 2022 - 2:00pm for 1 hour (actually 50 minutes)
Ryan Dickmann – Georgia Tech
Roberta Shapiro

This talk will focus on surfaces (orientable connected 2-manifolds) with noncompact boundary. Since a general surface with noncompact boundary can be extremely complicated, we will first consider a particular class called Sliced Loch Ness Monsters. We will discuss how to show the mapping class group of any Sliced Loch Ness Monster is uniformly perfect and automatically continuous. Depending on the time remaining, we will also discuss the classification of surfaces with noncompact boundary due to Brown and Messer, and how Sliced Loch Ness Monsters are used to prove results about the mapping class groups of general surfaces.