Geb. 20.30 SR 2.058

30. 03. 2023

Michał Marcinkowski

15:45 Uhr

Abstract: Let M be a compact Riemannian manifold. There are a number of interesting metrics on the group of volume preserving diffeomorphisms of M, among them the L¹-metric. If M is an (n>2)-dimensional disc, then the diameter of Diff₀(M,vol) with L¹-metric is finite by the celebrated result of A. Shnirelman. In the 2-dimensional case the situation is very different. In this talk I will show how to use braids to estimate the L¹-metric on Diff₀(M,area) where M is a compact surface. An an application we construct many L¹-Lipschitz quasimorphismsm on Diff₀(M,area) and show that all right-angled Artin groups embed quasi-isometrically into Diff₀(M,area). Joint work with M.Brandenbursky and E.Shelukhin.