University of Arkansas Topology Seminar: 2/7/2019

Speaker: Yo'av Rieck

Title: Gromov's topological overlap theorem

In this expository talk we will state and prove Gromov's topological overlap theorem. Roughly speaking, Gromov proved the existence of a constant μ > 0 so that with the following set-up:

1. X is a d–dimensional complex (satisfying certain conditions that will be explained in the talk) with n d–cells;
2. M is a d–dimensional PL-manifold; and
3. f : X → M is a continuous map,

there is a point in M with μ⋅n preimages.

The talk is based on the short paper On expansion and topological overlap by Dominic Dotterrer, Tali Kaufman, and Uli Wagner (Geom. Dedicata 195 (2018), 307–317).