# An annular refinement of the transverse element in Khovanov homology

@article{Hubbard2016AnAR,
title={An annular refinement of the transverse element in Khovanov homology},
author={Diana D. Hubbard and Adam Saltz},
journal={Algebraic & Geometric Topology},
year={2016},
volume={16},
pages={2305-2324}
}
• Published 2016
• Mathematics
• Algebraic & Geometric Topology
• We construct a braid conjugacy class invariant $\kappa$ by refining Plamenevskaya's transverse element $\psi$ in Khovanov homology via the annular grading. While $\kappa$ is not an invariant of transverse links, it distinguishes some braids whose closures share the same classical invariants but are not transversely isotopic. Using $\kappa$ we construct an obstruction to negative destabilization (stronger than $\psi$) and a solution to the word problem in braid groups. Also, $\kappa$ is a lower… CONTINUE READING

#### Citations

##### Publications citing this paper.
SHOWING 1-8 OF 8 CITATIONS

## A note on the transverse invariant from Khovanov homology

• Mathematics
• 2018

## Annular Khovanov-Lee homology, braids, and cobordisms

• Mathematics
• 2016
VIEW 6 EXCERPTS
CITES METHODS
HIGHLY INFLUENCED

## Annular link invariants from the Sarkar-Seed-Szab\'o spectral sequence.

• Mathematics
• 2019

## A note on the knot Floer homology of fibered knots

• Mathematics
• 2018

VIEW 2 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

## Khovanov homology and categorification of skein modules

• Mathematics
• 2018
VIEW 2 EXCERPTS
CITES BACKGROUND

## Invariants of transverse and annular links in combinatorial link Floer homology

• 2019
VIEW 3 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 34 REFERENCES

## On transverse invariants from Khovanov homology

• Mathematics
• 2015

## Categorification of the Kauffman bracket skein module of $I$–bundles over surfaces

• Mathematics
• 2004

## Computing annular Khovanov homology

• Mathematics
• 2015

## Khovanov homology, open books, and tight contact structures

• Mathematics
• 2008

## Algebraic Torsion in Contact Manifolds

• Mathematics
• 2011

## On Gradings in Khovanov homology and sutured Floer homology

• Mathematics
• 2010

## On the Heegaard Floer homology of branched double-covers

• Mathematics
• 2003