On bordered theories for Khovanov homology

Manion, Andrew

doi:10.2140/agt.2017.17.1557

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On bordered theories for Khovanov homology

Andrew Manion

Algebraic & Geometric Topology 17 (2017) 1557–1674

DOI: 10.2140/agt.2017.17.1557

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 $ℬ Γ_{n}$ , in terms of Khovanov’s theory of modules over the ring $H^{n}$ . 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 $H^{n}$ 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/

Volume 17, issue 3 (2017)