Davis manifolds: how they are constructed, how they can be compared, and how to study their simplicial volumes
Data: 10 GIUGNO 2025 dalle 11:15 alle 13:00
Luogo: aula Vitali, ore 11:15
We will start by revising an elegant construction of Davis, which is a powerful method for building manifolds with interesting, and sometimes surprising, properties. The input needed in order to produce a manifold is a triangulation of a sphere; the combinatorics of the triangulation dictates the topology of the produced manifold.
These manifolds constitute a rich set of examples for which various conjectures can be tested; specifically, we will consider a question of Gromov about two manifold invariants: the Euler characteristic and the simplicial volume. The approach that I present is based on the definition and study of a partial order on the set of triangulations of a sphere. Among other things, beautiful results from graph minors theory will appear during the talk.