Sutured Khovanov homology, Hochschild homology, and the Ozsváth-Szabó spectral sequence

Abstract

In 2002, Khovanov-Seidel constructed a faithful action of the ( m + 1 ) (m+1) –strand braid group, B m + 1 \mathfrak {B}_{m+1} , on the derived category of left modules over a quiver algebra, A m A_m . We interpret the Hochschild homology of the Khovanov-Seidel braid invariant as a direct summand of the sutured Khovanov homology of the annular braid closure.