Chirally cosmetic surgeries and Casson invariants
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,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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