Annular link invariants from the Sarkar-Seed-Szab\'o spectral sequence

Linh Truong; Melissa Zhang

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arXiv · 1909.05191

Annular link invariants from the Sarkar-Seed-Szab\'o spectral sequence

Linh Truong·Melissa Zhang

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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-Szab\'o'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.

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Linh Truong, Melissa Zhang. 2019-09-08. Annular link invariants from the Sarkar-Seed-Szab\'o spectral sequence. https://arxiv.org/abs/1909.05191

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