On bordered theories for Khovanov homology

Andrew Manion

doi:10.2140/agt.2017.17.1557

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arXiv · 1509.07174

On bordered theories for Khovanov homology

Andrew Manion

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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 $\mathcal{B}Γ_n$, 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.

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Andrew Manion. 2015-09-23. On bordered theories for Khovanov homology. https://doi.org/10.2140/agt.2017.17.1557

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