The L^1metric on Diff_0(M,area)

Venue:
Geb. 20.30 SR 2.058

Date:
30.03.2023

Speaker:
Michał Marcinkowski

Time:
15:45

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 L^{1}metric. If M is an (n>2)dimensional disc, then the diameter of Diff_{0}(M,vol) with L^{1}metric is finite by the celebrated result of A. Shnirelman. In the 2dimensional case the situation is very different. In this talk I will show how to use braids to estimate the L^{1}metric on Diff_{0}(M,area) where M is a compact surface. An an application we construct many L^{1}Lipschitz quasimorphismsm on Diff_{0}(M,area) and show that all rightangled Artin groups embed quasiisometrically into Diff_{0}(M,area). Joint work with M.Brandenbursky and E.Shelukhin.