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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On bordered theories for Khovanov homology

Andrew Manion

Algebraic & Geometric Topology 17 (2017) 1557–1674
Abstract

We describe how to formulate Khovanov’s functor-valued invariant of tangles in the language of bordered Heegaard Floer homology. We then give an alternate construction of Lawrence Roberts’ type D and type A structures in Khovanov homology, and his algebra Γn, in terms of Khovanov’s theory of modules over the ring Hn. We reprove invariance and pairing properties of Roberts’ bordered modules in this language. Along the way, we obtain an explicit generators-and-relations description of Hn which may be of independent interest.

Keywords
Khovanov homology, bordered Floer homology, invariants of tangles, linear-quadratic algebras
Mathematical Subject Classification 2010
Primary: 57M27
References
Publication
Received: 12 November 2015
Revised: 13 July 2016
Accepted: 2 September 2016
Published: 17 July 2017
Authors
Andrew Manion
Department of Mathematics
UCLA
520 Portola Plaza
Los Angeles, CA 90095
United States
http://math.ucla.edu/~manion/