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Homomorphisms of pure mapping class groups to the integers

Priyam Patel, UCSD
Tuesday, October 16, 2018 - 1:30pm to 3:30pm
PDL C-401

Abstract. 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.