Geodesic
A type A structure in Khovanov homology
Roberts, Lawrence1
1Department of Mathematics, University of Alabama, Box 870350, Tuscaloosa, AL 35487-0350, United States
Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3653-3719
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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.

DOI : 10.2140/agt.2016.16.3653
Classification : 57M27, 55N35
Keywords: Khovanov homology, bordered theory, tangle invariant

Roberts, Lawrence  1

1 Department of Mathematics, University of Alabama, Box 870350, Tuscaloosa, AL 35487-0350, United States 
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Roberts, Lawrence. A type A structure in Khovanov homology. Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3653-3719. doi: 10.2140/agt.2016.16.3653

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