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.
From: Aakash Parikh [view email]
[v1]
Sat, 20 Jun 2026 02:00:34 UTC (58 KB)
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