分野別セミナー

Unlike the Burau representation of the braid group itself, it is known that Khovanov-Seidel's categorified Burau representation by is faithful. In this talk, we present several simple observations on how to read the Dehornoy ordering, or Garside length of braids from Khovanov-Seidel categorified Burau representation, based on the deep result that the categorified action detects the geometric intersection number of arcs in punctured disk. For example, we explain that the homological grading is closely related to Garside structure of braids.