Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 6 (2016), 3653-3719.
A type $A$ structure in Khovanov homology
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.
Algebr. Geom. Topol., Volume 16, Number 6 (2016), 3653-3719.
Received: 1 April 2016
Accepted: 18 April 2016
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Roberts, Lawrence. A type $A$ structure in Khovanov homology. Algebr. Geom. Topol. 16 (2016), no. 6, 3653--3719. doi:10.2140/agt.2016.16.3653. https://projecteuclid.org/euclid.agt/1510841273