2025 Obstructing Reducible Surgeries: Slice Genus and Thickness Bounds
Holt Bodish, Robert DeYeso III
Michigan Math. J. Advance Publication 1-20 (2025). DOI: 10.1307/mmj/20226325

Abstract

In this paper, we study reducible surgeries on knots in S3. We develop thickness bounds for L-space knots that admit reducible surgeries and lower bounds on the slice genus for general knots that admit reducible surgeries. The lower bound on thickness for L-space knots allows us to finish off the verification of the cabling conjecture for thin knots, which was mostly worked out in [DeY21]. We also provide a new upper bound on reducing slopes for fibered, hyperbolic slice knots and on multiple reducing slopes for slice knots. Our techniques involve the d-invariants and mapping cone formula from Heegaard Floer homology.

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Holt Bodish. Robert DeYeso III. "Obstructing Reducible Surgeries: Slice Genus and Thickness Bounds." Michigan Math. J. Advance Publication 1 - 20, 2025. https://doi.org/10.1307/mmj/20226325

Information

Received: 12 December 2022; Revised: 4 September 2024; Published: 2025
First available in Project Euclid: 23 January 2025

Digital Object Identifier: 10.1307/mmj/20226325

Keywords: 57K10

Rights: Copyright © 2024 The University of Michigan

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