Volume 16, issue 4 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 4, 1827–2458
Issue 3, 1253–1825
Issue 2, 621–1251
Issue 1, 1–620

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
An annular refinement of the transverse element in Khovanov homology

Diana Hubbard and Adam Saltz

Algebraic & Geometric Topology 16 (2016) 2305–2324

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.

Khovanov homology, transverse knot, invariant, braids
Mathematical Subject Classification 2010
Primary: 20F36, 57M25, 57M27, 57R17
Received: 4 August 2015
Revised: 11 November 2015
Accepted: 4 December 2015
Published: 12 September 2016
Diana Hubbard
Department of Mathematics
Boston College
Maloney Hall, Fifth Floor
Chestnut Hill, MA 02467-3806
United States
Adam Saltz
Department of Mathematics
Boston College
Maloney Hall, Fifth Floor
Chestnut Hill, MA 02467-3806
United States