Alternating odd pretzel knots and chirally cosmetic surgeries

Konstantinos Varvarezos

doi:10.1142/s0218216522500456

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arXiv · 2003.08442

Alternating odd pretzel knots and chirally cosmetic surgeries

Konstantinos Varvarezos

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Abstract

A pair of surgeries on a knot is chirally cosmetic if they result in homeomorphic manifolds with opposite orientations. Using recent methods of Ichihara, Ito, and Saito, we show that, except for the (2,5) and (2,7)-torus knots, the genus 2 and 3 alternating odd pretzel knots do not admit any chirally cosmetic surgeries. Further, we show that for a fixed genus, at most finitely many alternating odd pretzel knots admit chirally cosmetic surgeries.

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Konstantinos Varvarezos. 2020-03-18. Alternating odd pretzel knots and chirally cosmetic surgeries. https://doi.org/10.1142/s0218216522500456

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