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 ${\rm SL}(2,\mathbb{C})$ version of Casson invariants. As applications, we give a complete classification of chirally cosmetic surgeries on alternating knots of genus one.
Citation
Kazuhiro ICHIHARA. Tetsuya ITO. Toshio SAITO. "Chirally Cosmetic Surgeries and Casson Invariants." Tokyo J. Math. 44 (1) 1 - 24, June 2021. https://doi.org/10.3836/tjm/1502179325
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