Annular Khovanov–Lee homology, braids, and cobordisms

Autor:	Anthony Licata, Stephan M. Wehrli, J. Elisenda Grigsby
Rok vydání:	2017
Předmět:	Pure mathematics General Mathematics Homotopy Braid Isotopy Homology (mathematics) Invariant (mathematics) Nonlinear Sciences::Pattern Formation and Solitons Mathematics::Symplectic Geometry Mathematics::Geometric Topology Mathematics
Zdroj:	Pure and Applied Mathematics Quarterly. 13:389-436
ISSN:	1558-8602 1558-8599
DOI:	10.4310/pamq.2017.v13.n3.a2
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8d856b3d5b97167874aea956e2449c2a https://doi.org/10.4310/pamq.2017.v13.n3.a2 Zobrazit plný text záznamu