The fractional Dehn twist coefficient of braids and homogenizations of knot invariants

Vortrag von Dr. Peter Feller

Datum: 27.09.17  Zeit: 15.45 - 16.45  Raum: ETH HG G 43

We discuss connections between two different points of view on Artin's braid groups: braids as mapping classes of punctured discs and braids as a tool to study knots via the closure operation. Our main result is a characterization of the `fractional Dehn twist coefficient' of braids — a rational number associated with a mapping class first introduced by Gabai and Oertel — in terms of knot invariants due to Ozsvath, Stipsicz, and Szabo. We provide consequences about the complexity of braids (and knots that arise as their closure) for braids with `many twists'. A key ingredient for the characterization are homogeneous quasi-morphisms on braid groups that arise from knot invariants.