"Geometry and Analysis on Groups" Research Seminar
Time: 2015.11.17, 15:00–17:00
Location: Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Higher-dimensional expansion and topological overlap."
Wagner (Institute of Science and Technology Austria)
In the first part of the talk, we give an introduction to higher-dimensional expansion properties
of cell complexes. A special focus will be on the notion of coboundary expansion (informally:
the existence of a linear isoperimetric inequality for the cellular coboundary operator),
which was introduced independently by Linial & Meshulam and by Gromov and which
generalizes the classical notion of edge expansion of graphs.
In the second part of the talk, we will present a simple proof of Gromov's Topological Overlap Theorem:
If \(X\) is a \(d\)–dimensional complex which is a coboundary expander in dimensions \(1,2,\dots d\),
then for every continuous map \(f\colon\thinspace X\to M\) into a \(d\)–dimensional PL manifold, there exists an
image point \(p\in M\) that is covered by the \(f\)–images of a
constant fraction of the \(d\)–simplices of \(M\).
(Joint work with Dotterrer and Kaufman)