A type A structure in Khovanov homology

作者：Roberts Lawrence P^*

来源：Algebraic and Geometric Topology, 2016, 16(6): 3653-3719.

DOI：10.2140/agt.2016.16.3653

Inspired by bordered Floer homology, we describe a type A structure in Khovanov homology, which complements the type D structure previously defined by the author. The type A structure is a differential module over a certain algebra. This can be paired with the type D structure to recover the Khovanov chain complex. The homotopy type of the type A structure is a tangle invariant, and homotopy equivalences of the type A 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.

• 出版日期2016