Séminaire Cirget

Braids, quasimorphisms, and slice-Bennequin inequalities

Conférencier: Peter Feller, ETH Zurich

Résumé / Abstract: The writhe of a braid (=#pos crossing - #neg crossings) and the fractional Dehn twist coefficient of a braid (a rational number that measures "how much the braid twists") are the two most prominent examples of what is known as a quasimorphism (a map that fails to be a group homomorphism by at most a bounded amount) from Artin's braid group on n-strands to the reals. We consider characterizing properties for such quasimorphisms and talk about relations to the study of knot concordance. For the latter, we consider inequalities for quasimorphisms modelled after the so-called slice-Bennequin inequality: writhe(B) <= 2g_4(K) - 1 + n for all n-stranded braids B with closure a knot K. Based on work in progress.

Le lien pour se connecter est: https://uqam.zoom.us/j/98999725241