Abstract
Inspired by bordered Floer homology, we describe a type structure in Khovanov homology, which complements the type structure previously defined by the author. The type structure is a differential module over a certain algebra. This can be paired with the type structure to recover the Khovanov chain complex. The homotopy type of the type structure is a tangle invariant, and homotopy equivalences of the type structure result in chain homotopy equivalences on the Khovanov chain complex found from a pairing. We use this to simplify computations and introduce a modular approach to the computation of Khovanov homologies. Several examples are included, showing in particular how this approach computes the correct torsion summands for the Khovanov homology of connect sums. A lengthy appendix is devoted to establishing the theory of these structures over a characteristic-zero ring.
Citation
Lawrence Roberts. "A type $A$ structure in Khovanov homology." Algebr. Geom. Topol. 16 (6) 3653 - 3719, 2016. https://doi.org/10.2140/agt.2016.16.3653
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