A surgery formula for knot Floer homology

DOI10.4171/QT/188arXiv1901.02488OpenAlexW2908718270WikidataQ130072522 ScholiaQ130072522MaRDI QIDQ6203833

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Publication date: 8 April 2024

Published in: (Search for Journal in Brave)

Abstract: Let $K$ be a rationally null-homologous knot in a $3$-manifold $Y$, equipped with a nonzero framing $lambda$, and let $Y_{l}ambda(K)$ denote the result of $lambda$-framed surgery on $Y$. Ozsv'ath and Szab'o gave a formula for the Heegaard Floer homology groups of $Y_{l}ambda(K)$ in terms of the knot Floer complex of $(Y,K)$. We strengthen this formula by adding a second filtration that computes the knot Floer complex of the dual knot $K_{l}ambda$ in $Y_{l}ambda$, i.e., the core circle of the surgery solid torus. In the course of proving our refinement we derive a combinatorial formula for the Alexander grading which may be of independent interest.

Full work available at URL: https://arxiv.org/abs/1901.02488

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