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2016 A type $A$ structure in Khovanov homology
Lawrence Roberts
Algebr. Geom. Topol. 16(6): 3653-3719 (2016). 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.


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Lawrence Roberts. "A type $A$ structure in Khovanov homology." Algebr. Geom. Topol. 16 (6) 3653 - 3719, 2016.


Received: 1 April 2016; Accepted: 18 April 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1360.57026
MathSciNet: MR3584271
Digital Object Identifier: 10.2140/agt.2016.16.3653

Primary: 57M27
Secondary: 55N35

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 6 • 2016
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