An Alexander method for infinite-type surfaces

Geometry Topology Student Seminar
Wednesday, November 17, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Online (via BlueJeans)
Roberta Shapiro – Georgia Tech
Roberta Shapiro and Weizhe Shen

Please Note: BlueJeans link:

Given a surface S, the Alexander method is a combinatorial tool used to determine whether two self-homeomorphisms of S are isotopic. This statement was formalized in the case of finite-type surfaces, which are surfaces with finitely generated fundamental groups. A version of the Alexander method was extended to infinite-type surfaces by Hernández-Morales-Valdez and Hernández-Hidber. We extend the remainder of the Alexander method to include infinite-type surfaces. 


In this talk, we will talk about several applications of the Alexander method. Then, we will discuss a technique useful in proofs dealing with infinite-type surfaces and provide a "proof by example" of an infinite-type analogue of the Alexander method.

This will be practice for a future talk and comments and suggestions are appreciated.