Right-angledness, flag complexes, asphericity

Right-angledness, flag complexes, asphericity

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Mike Davis, Ohio State University and IAS
Fine Hall 314

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 and 2) the Borel-Serre bordification of torsion-free arithmetic groups which are nonuniform lattices.