The L^1-metric on Diff_0(M,area)
Geb. 20.30 SR 2.058
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.