Annular khovanov-lee homology, braids, and cobordisms

We prove that the Khovanov-Lee complex of an oriented link, L, in a thickened annulus, A × I, has the structure of a (forumala presented).–filtered complex whose filtered chain homotopy type is an invariant of the isotopy class of L ⊂ (A × I). Using ideas of Ozsváth-Stipsicz-Szabó [34] as reinterpreted by Livingston [30], 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.