Sutured Khovanov homology, Hochschild homology, and the Ozsvath-Szabo spectral sequence
Denis Auroux, J. Elisenda Grigsby, Stephan M. Wehrli
TL;DR
This paper explores the relationship between sutured Khovanov homology, Hochschild homology, and the Ozsvath-Szabo spectral sequence, revealing new insights into braid group actions and link invariants.
Contribution
It interprets Hochschild homology of the Khovanov-Seidel invariant as a summand of sutured Khovanov homology, connecting algebraic and topological invariants.
Findings
Hochschild homology corresponds to a summand of sutured Khovanov homology.
Provides a new perspective on the braid group action in link invariants.
Links algebraic structures with topological invariants through spectral sequences.
Abstract
In 2001, Khovanov and Seidel constructed a faithful action of the (m+1)-strand braid group on the derived category of left modules over a quiver algebra, 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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology