A note on the knot Floer homology of freely 2-periodic knots and their quotients

Timothy Bates; Aakash Parikh

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arXiv · 2606.21834

A note on the knot Floer homology of freely 2-periodic knots and their quotients

Timothy Bates·Aakash Parikh

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Abstract

A knot P in the three-sphere is freely 2-periodic if it is preserved setwise by a free order-two action. There is a natural projective quotient knot associated to P. We establish a rank inequality between the knot Floer homologies of P and its quotient as a consequence of Large's generalization of Seidel--Smith's localization spectral sequence associated to order 2 actions in Lagrangian Floer homology. As a corollary we obtain an inequality between the Seifert genus of P and the rational Seifert genus of its quotient. We also implement a program which computes the E2 page of this spectral sequence using a modification of Baldwin--Gillam's grid homology calculator.

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Timothy Bates, Aakash Parikh. 2026-06-20. A note on the knot Floer homology of freely 2-periodic knots and their quotients. https://arxiv.org/abs/2606.21834

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