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On constraints for knots to admit chirally cosmetic surgeries and their calculations (2112.04156v2)
Published 8 Dec 2021 in math.GT
Abstract: We discuss various constraints for knots in $S{3}$ to admit chirally cosmetic surgeries, derived from invariants of 3-manifolds, such as, the quantum $SO(3)$-invariant, the rank of the Heegaard Floer homology, and finite type invariants. We apply them to show that a large portion (roughly 75$\%$) of knots which are neither amphicheiral nor $(2,p)$-torus knots with less than or equal to 10 crossings admits no chirally cosmetic surgeries.