Annular Link Invariants from the Sarkar–Seed–Szabó Spectral Sequence

Abstract

For a link in a thickened annulus $\mathit{A}\times \mathit{I}$, we define a $\mathbb{Z}\oplus \mathbb{Z}\oplus \mathbb{Z}$ filtration on Sarkar–Seed–Szabó’s perturbation of the geometric spectral sequence. The filtered chain homotopy type is an invariant of the isotopy class of the annular link. From this, we define a two-dimensional family of annular link invariants and study their behavior under cobordisms. In the case of annular links obtained from braid closures, we obtain a necessary condition for braid quasi-positivity and a sufficient condition for right-veeringness, as well as Bennequin-type inequalities.