Obstructing Reducible Surgeries: Slice Genus and Thickness Bounds

Holt Bodish; Robert DeYeso III

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arXiv · 2209.01672

Obstructing Reducible Surgeries: Slice Genus and Thickness Bounds

Holt Bodish·Robert DeYeso III

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Abstract

In this paper, we study reducible surgeries on knots in $S^3$. 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 L-space knot thickness bounds allow us to finish off the verification of the Cabling Conjecture for thin knots, which was mostly worked out in \cite{DeY21b}. 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. 2022-09-04. Obstructing Reducible Surgeries: Slice Genus and Thickness Bounds. https://arxiv.org/abs/2209.01672

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