For a link in a thickened annulus , we define a 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.
"Annular Link Invariants from the Sarkar–Seed–Szabó Spectral Sequence." Michigan Math. J. 71 (4) 725 - 763, November 2022. https://doi.org/10.1307/mmj/20205862