On transverse invariants from Khovanov homology


Journal Article

© European Mathematical Society. In [31], O. Plamenevskaya associated to each transverse knot K an element of the Khovanov homology of K. In this paper, we give two re_nements of Plamenevskaya’s invariant, one valued in Bar-Natan’s deformation (from [2]) of the Khovanov complex and another as a cohomotopy element of the Khovanov spectrum (from [20]). We show that the first of these refinements is invariant under negative flypes and SZ moves; this implies that Plamenevskaya’s class is also invariant under these moves. We go on to show that for small-crossing transverse knots K, both re_nements are determined by the classical invariants of K.

Full Text

Duke Authors

Cited Authors

  • Lipshitz, R; Ng, L; Sarkar, S

Published Date

  • January 1, 2015

Published In

Volume / Issue

  • 6 / 3

Start / End Page

  • 475 - 513

Electronic International Standard Serial Number (EISSN)

  • 1664-073X

International Standard Serial Number (ISSN)

  • 1663-487X

Digital Object Identifier (DOI)

  • 10.4171/QT/69

Citation Source

  • Scopus