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2016 An annular refinement of the transverse element in Khovanov homology
Diana Hubbard, Adam Saltz
Algebr. Geom. Topol. 16(4): 2305-2324 (2016). DOI: 10.2140/agt.2016.16.2305


We construct a braid conjugacy class invariant κ by refining Plamenevskaya’s transverse element ψ in Khovanov homology via the annular grading. While κ is not an invariant of transverse links, it distinguishes some braids whose closures share the same classical invariants but are not transversely isotopic. Using κ we construct an obstruction to negative destabilization (stronger than ψ) and a solution to the word problem in braid groups. Also, κ is a lower bound on the length of the spectral sequence from annular Khovanov homology to Khovanov homology, and we obtain concrete examples in which this spectral sequence does not collapse immediately. In addition, we study these constructions in reduced Khovanov homology and illustrate that the two reduced versions are fundamentally different with respect to the annular filtration.


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Diana Hubbard. Adam Saltz. "An annular refinement of the transverse element in Khovanov homology." Algebr. Geom. Topol. 16 (4) 2305 - 2324, 2016.


Received: 4 August 2015; Revised: 11 November 2015; Accepted: 4 December 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 1366.57004
MathSciNet: MR3546466
Digital Object Identifier: 10.2140/agt.2016.16.2305

Primary: 20F36 , 57M25 , 57M27 , 57R17

Keywords: braids , invariant , Khovanov homology , transverse knot

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 4 • 2016
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