Rank Inequalities on Knot Floer Homology of Periodic Knots

Keegan Boyle

doi:10.1112/blms.12595

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arXiv · 1810.01526

Rank Inequalities on Knot Floer Homology of Periodic Knots

Keegan Boyle

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Abstract

Let $\widetilde{K}$ be a 2-periodic knot in $S^3$ with quotient $K$. We prove a rank inequality between the knot Floer homology of $\widetilde{K}$ and the knot Floer homology of $K$ using a spectral sequence of Hendricks, Lipshitz and Sarkar. We also conjecture a filtered refinement of this inequality, for which we give computational evidence, and produce applications to the Alexander polynomials of $\widetilde{K}$ and $K$.

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BibTeX RIS

Keegan Boyle. 2018-10-02. Rank Inequalities on Knot Floer Homology of Periodic Knots. https://doi.org/10.1112/blms.12595

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