Date: Thursday, February 01, 2018
Location: 1866 East Hall (5:00 PM to 6:00 PM)
Title: Normal generators for mapping class groups are abundant
Abstract: Under what conditions do a group element and all of its conjugates form a generating set for the ambient group? Such an element is called a normal generator. For mapping class groups of surfaces, we give a number of geometric criteria that ensure that a mapping class is a normal generator. With these criteria in hand, we show that every nontrivial periodic element in a mapping class group (except for a hyperelliptic involution) is a normal generator. We also show that if the stretch factor of a pseudoAnosov mapping class is sufficiently small, then it is a normal generator. Our pseudoAnosov examples answer a question of Darren Long from 1986. This is joint work with Dan Margalit.
Files:
Speaker: Justin Lanier
Institution: Georgia Tech
Event Organizer: Nicholas Vlamis vlamis@umich.edu
