Speaker: Bruno Bendedetti (KTH)
Title: METRIC GEOMETRY AND COLLAPSIBILITY
Abstract:

A simplicial complex can be turned into a (piece-wise Euclidean) metric
space by assigning the same length to all edges. We show that if a
complex becomes a CAT(0) metric space with this metric, then it is
combinatorially collapsible. This is a discrete analog of the classical
theorem that
CAT(0) complexes are contractible. As an application, we construct some
manifolds different than balls that admit a collapsible triangulation.
This contrasts a 1939 result of Whitehead. Also, it shows that discrete
Morse theory can be sharper than smooth Morse theory in bounding the
homology of a manifold.

If time permits, we discuss extensions to different metrics and
applications to Hirsch diameter bounds.

This is joint work with Karim Adiprasito (http://arxiv.org/abs/1107.5789).