Title: On the braid index and the fractional Dehn twist coefficient

Date: 09/14/2017

Time: 2:00 PM - 3:00 PM

Place: C304 Wells Hall

Speaker: Diana Hubbard, University of Michigan

The braid index of a knot is the least number of strands necessary to represent the knot as a closure of a braid on that many strands. If we view a braid as an element of the mapping class group of the punctured disk, its fractional Dehn twist coefficient (FDTC) is a number that measures the amount of twisting it exerts about the boundary of the disk. In this talk I will demonstrate that n-braids with FDTC larger than n-1 realize the braid index of their closure. The proof uses the concordance homomorphism Upsilon arising from knot Floer homology as a crucial tool. This is joint work with Peter Feller.