The braid index of highly twisted braid closures

Diana Hubbard (CUNY)

Abstract: The braid index of a knot is the least number of strands necessary to represent it as the closure of a braid. If we view a braid as an element of the mapping class group of the punctured disk, its fractional Dehn twist coefficient measures, informally, the amount of twisting it exerts about the boundary. In this talk I will discuss joint work with Peter Feller showing that if an n-braid has fractional Dehn twist coefficient greater than n-1, then its closure is of minimal braid index, which draws a connection between braids as topological and geometric objects.