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 discuss non-existence for chirally cosmetic surgeries on almost positive knots, and we give a complete classification of chirally cosmetic surgeries on two bridge knots of genus one. 查看全文>>