Normal generators for mapping class groups are abundant

Wednesday, April 10, 2019 - 15:00 to 16:00

Thackeray 427

Speaker Information
Justin Lanier
Georgia Tech

Abstract or Additional Information

We'll begin by giving an introduction to mapping class groups of surfaces, which play an important role in low-dimensional topology, geometric group theory, and other fields. We'll then describe a number of simple criteria that ensure that a mapping class group element is a normal generator, that is, its normal closure is the whole group. We apply these criteria to show that almost every periodic element is a normal generator whenever genus is at least 3.  We also show that every pseudo-Anosov element with stretch factor less than √2 is a normal generator. Our pseudo-Anosov results answer a question of Long from 1986. This is joint work with Dan Margalit.