Bonn Topology Group - Abstracts

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Talk

October 15th 2019
Steffen Kionke (KIT, Karlsruhe): Limits of topological invariants in the p-adic numbers

Abstract

We introduce new invariants of topological spaces: the p-adic Betti numbers and the p-adic torsion. These invariants are p-adic limits of classical topological invariants and are, in this respect, similar to L^2-invariants. In other aspects, however, the p-adic invariants behave like antagonists of L^2-invariants. For instance, p-adic Betti numbers can distinguish certain amenable groups, but are equal for all free groups. We discuss some examples and open problems and we explain how the p-adic Betti numbers can be used to study the growth of ordinary Betti numbers in towers of finite sheeted covering spaces.

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