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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2015
- DOI:
- 10.48550/arXiv.1509.07174
- arXiv:
- arXiv:1509.07174
- Bibcode:
- 2015arXiv150907174M
- Keywords:
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- Mathematics - Geometric Topology;
- 57M27
- E-Print:
- 87 pages