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arXiv · 1707.00152

Chirally cosmetic surgeries and Casson invariants

Kazuhiro Ichihara·Tetsuya Ito·Toshio Saito
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Abstract

We study chirally cosmetic surgeries, that is, a pair of Dehn surgeries on a knot producing homeomorphic 3-manifolds with opposite orientations. Several constraints on knots and surgery slopes to admit such surgeries are given. Our main ingredients are the original and the $SL(2,\mathbb{C})$ version of Casson invariants. As applications, we give a complete classification of chirally cosmetic surgeries on alternating knots of genus one.

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Kazuhiro Ichihara, Tetsuya Ito, Toshio Saito. 2019-02-27. Chirally cosmetic surgeries and Casson invariants. https://arxiv.org/abs/1707.00152

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