On bordered theories for Khovanov homology

Abstract

We describe how to formulate Khovanov's functor-valued invariant of tangles in the language of bordered Heegaard Floer homology. We then give an alternate construction of Lawrence Roberts' Type D and Type A structures in Khovanov homology, and his algebra $\mathcal{B}{\Gamma }_n$, in terms of Khovanov's theory of modules over the ring $H^n$. We reprove invariance and pairing properties of Roberts' bordered modules in this language. Along the way, we obtain an explicit generators-and-relations description of $H^n$ which may be of independent interest.

87 pages; 2 figures

References in corpus (2)

• A type A structure in Khovanov Homology
• A type D structure in Khovanov homology

Cited by in corpus (2)

• Immersed curves in Khovanov homology
• The Fukaya category of the pillowcase, traceless character varieties, and Khovanov Cohomology