Annular link invariants from the Sarkar-Seed-Szabó spectral sequence

Abstract

For a link in a thickened annulus $A\times I$, 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 quasipositivity and a sufficient condition for right-veeringness, as well as Bennequin-type inequalities.

33 pages, 9 figures. arXiv admin note: text overlap with arXiv:1612.05953 by other authors