Priyam Patel, UCSD

PDL C401
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, finitetype surface of genus at least 3 is perfect, that is, it has trivial abelianization. We will discuss how this fails for infinitegenus surfaces and give a complete characterization of all homomorphisms from pure mapping class groups of infinitegenus surfaces to the integers. This is joint work with Javier Aramayona and Nicholas Vlamis.