Handlebody mapping class groups are virtual duality groups

Ric Wade (University of Oxford)

Monday 10th March 16:00-17:00 Maths 311B

Abstract

In the 1970's Bieri and Eckmann defined a notion of duality for discrete groups which can be thought of as a version of Poincaré duality with twisted coefficients. Many discrete groups that appear in geometric topology are known to be duality groups, and we add to this list by proving that the same is true for mapping class groups of handlebodies. There are two key steps: construction of a contractible submanifold of Teichmüller space on which the handlebody group acts properly and cocompactly, and an analysis of the topology of this manifold's boundary.  Roughly speaking, the construction is a lift of a classifying space of the handelbody group built by Hainaut and Petersen inside moduli space, and is joint work with Dan Petersen.

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