Braids, quasimorphisms, and slice-Bennequin inequalities

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.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

[[Please leave your micro off when entering the seminar room and provide your family name and first name in order to be identified by the speaker.]]

The livestream is on Zoom at : uqam.zoom.us/j/98999725241 (no password is needed).

The recorded talks can be found at CIRGET channel : www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA