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Topology/Geometry Seminar

 Exploring algebraic rigidity in mapping class groups 

Nicholas Vlamis (CUNY)

Location:  Hill 005
Date & time: Tuesday, 09 April 2019 at 3:30PM - 4:30PM

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 characterization yields a direct connection between algebraic invariants of pure mapping class groups and topological invariants of the underlying surface.

This is joint work with Javier Aramayona and Priyam Patel.

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