Hebrew University topology and geometry seminar

Abstract: We use a geometric idea to give an analytic estimate for the word-length in the pure braid group of $S^{2}$. This yields that the $L^{1}$-norm (and hence each $L^{p}$-norm, including $L^{2}$) on the group of area-preserving diffeomorphisms of $S^{2}$ is unbounded. This solves an open question arising from the work of Shnirelman and Eliashberg-Ratiu. Joint work in progress with Michael Brandenbursky.