Speaker: Michael Dougherty

Title: Braids, Configurations, and Noncrossing Partitions

 

Abstract: There is a well-known relationship between the n-strand braid group and the complement of a set of hyperplanes in complex n-space. In 1987, Salvetti described a deformation retraction of this space which resulted in a finite cell complex with the same homotopy type. Another homotopy-equivalent complex was obtained by T. Brady in 2001 using a different presentation for the braid group, but without giving an explicit deformation retraction. In this talk I will describe such a homotopy equivalence for n=3 and discuss the situation for more strands.