Topology Seminar (Main Talk): Homomorphisms of pure mapping class groups to the integers

Seminar | February 21 | 4-5 p.m. | 3 Evans Hall

 Priyam Patel, University of California, Santa Barbara

 Department of Mathematics

A classical theorem of Powell (with roots in the work of Mumford and Birman) states that the pure mapping class group of a connected, orientable, finite-type surface of genus at least 3 is perfect, that is, it has trivial abelianization. We will discuss how this fails for infinite-genus surfaces and give a complete characterization of all homomorphisms from pure mapping class groups of infinite-genus surfaces to the integers. This is joint work with Javier Aramayona and Nicholas Vlamis.