Braids, quasimorphisms, and slice-Bennequin inequalities.

Geometry Topology Seminar
Monday, February 8, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Peter Feller – ETH Zurich – peter.feller@math.ethz.ch
Siddhi Krishna

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 quasimorphism 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.