Research PaperNo Access

Alternating odd pretzel knots and chirally cosmetic surgeries

Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ, 08544-1000, USA

https://doi.org/10.1142/S0218216522500456Cited by:3 (Source: Crossref)

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.

Keywords:

AMSC: 57K10

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