Special alternating knots with sufficiently many twist regions have no chirally cosmetic surgeries

Tetsuya Ito

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arXiv · 2301.09855

Special alternating knots with sufficiently many twist regions have no chirally cosmetic surgeries

Tetsuya Ito

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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.

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Tetsuya Ito. 2023-01-24. Special alternating knots with sufficiently many twist regions have no chirally cosmetic surgeries. https://arxiv.org/abs/2301.09855

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