Annular Khovanov-Lee homology, braids, and cobordisms
Geometric Topology
2016-12-20 v1 Quantum Algebra
Representation Theory
Abstract
We prove that the Khovanov-Lee complex of an oriented link, L, in a thickened annulus, A x I, has the structure of a bifiltered complex whose filtered chain homotopy type is an invariant of the isotopy class of L in A x I. Using ideas of Ozsvath-Stipsicz-Szabo as reinterpreted by Livingston, we use this structure to define a family of annular Rasmussen invariants that yield information about annular and non-annular cobordisms. Focusing on the special case of annular links obtained as braid closures, we use the behavior of the annular Rasmussen invariants to obtain a necessary condition for braid quasipositivity and a sufficient condition for right-veeringness.
Keywords
Cite
@article{arxiv.1612.05953,
title = {Annular Khovanov-Lee homology, braids, and cobordisms},
author = {J. Elisenda Grigsby and Anthony M. Licata and Stephan M. Wehrli},
journal= {arXiv preprint arXiv:1612.05953},
year = {2016}
}
Comments
33 pages, 2 figures