Seminar February 8 – Mike Davis

After a brief hiatus the Geometry-Topology seminar returns with a talk by Mike Davis, from the Institute for Advanced Study, at 3:30 PM.

Title: Right-angledness, flag complexes, asphericity

Abstract: I will discuss three related constructions of spaces and manifolds and then give necessary and sufficient conditions for the resulting spaces to be aspherical. The first construction is the polyhedral product functor. The second construction involves applying the reflection group trick to a “corner of spaces”. The third construction involves pulling back a corner of spaces via a coloring of a simplicial complex. The two main sources of examples of corners which yield aspherical results are:

  1. Products of aspherical manifolds with (aspherical) boundary
  2. The Borel-Serre bordification of torsion-free arithmetic groups which are nonuniform lattices
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