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Special alternating knots with sufficiently many twist regions have no chirally cosmetic surgeries (2301.09855v1)
Published 24 Jan 2023 in math.GT
Abstract: We show that a special alternating knot with sufficiently large number (more than $63$) of twist regions has no chirally cosmetic surgeries, a pair of Dehn surgeries producing orientation-reversingly homeomorphic $3$-manifolds. In the course of proof, we provide the optimal upper bounds of the primitive finite type invariants of degree 2 and 3 that solve Willerton's conjecture.