Annular Khovanov-Lee homology, braids, and cobordisms

J. Elisenda Grigsby; Anthony M. Licata; Stephan M. Wehrli

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arXiv · 1612.05953

Annular Khovanov-Lee homology, braids, and cobordisms

J. Elisenda Grigsby·Anthony M. Licata·Stephan M. Wehrli

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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.

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BibTeX RIS

J. Elisenda Grigsby, Anthony M. Licata, Stephan M. Wehrli. 2016-12-18. Annular Khovanov-Lee homology, braids, and cobordisms. https://arxiv.org/abs/1612.05953

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