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}
}
  • Diana D. Hubbard, Adam Saltz
  • 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

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