Integer surgeries rational homology cobordant to lens spaces

Antony T. H. Fung

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arXiv · 2405.11736

Integer surgeries rational homology cobordant to lens spaces

Antony T. H. Fung

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Abstract

The Cyclic Surgery Theorem and Moser's work on surgeries on torus knots imply that for any non-trivial knot in $S^3$, there are at most two integer surgeries that produce a lens space. This paper investigates how many positive integer surgeries on a given knot in $S^3$ can produce a manifold rational homology cobordant to a lens space. Tools include Greene and McCoy's work on changemaker lattices which come from Heegaard Floer $d$-invariants, and Aceto-Celoria-Park's work on rational cobordisms and integral homology which is based on Lisca's work on lens spaces.

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BibTeX RIS

Antony T. H. Fung. 2024-05-20. Integer surgeries rational homology cobordant to lens spaces. https://arxiv.org/abs/2405.11736

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