Seminar Event Detail


Topology

Date:  Thursday, February 01, 2018
Location:  1866 East Hall (3:00 PM to 4:00 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 pseudo-Anosov mapping class is sufficiently small, then it is a normal generator. Our pseudo-Anosov examples answer a question of Darren Long from 1986. This is joint work with Dan Margalit.

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Speaker:  Justin Lanier
Institution:  Georgia Tech

Event Organizer:   Nicholas Vlamis    vlamis@umich.edu

 

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