Georgia Institute of Technology College of Sciences

Given a surface S, the Alexander method is a combinatorial tool used to determine whether two homeomorphisms are isotopic. This statement was formalized in A Primer on Mapping Class Groups in the case that S is of finite type. We extend the Alexander method to include infinite-type surfaces, which are surfaces with infinitely generated fundamental groups.

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