College of Liberal Arts & Sciences

# Topology Seminar

Speaker:

Peter Feller (ETH-Zurich)

Topic:

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.

Event Date:

February 16, 2021 - 2:30pm to 3:30pm

Location:

Online

Calendar Category:

Seminar

Seminar Category:

Geometry and Topology