Chirally cosmetic surgery conjecture for knots
Chirally cosmetic surgery conjecture for knots
Let be a knot in . Two surgeries on with distinct slopes are chirally cosmetic surgeries when , where the minus sign denotes orientation reversal. Chirally cosmetic surgery conjecture. A knot does not admit chirally cosmetic surgeries if it is not the unknot, a torus knot, or an amphichiral knot. The conjecture identifies the unknot, the specified torus knots, and amphichiral knots as the possible exceptions to the absence of chirally cosmetic surgeries; the source does not establish a general resolution.
Sources & referencesView supporting material
Primary source
Michael Huang, Zelong Li, Rahi Tanaz and Chengyi Zhang, “Positive 2-bridge knots and chirally cosmetic surgeries”, arXiv:2308.10126 (2023).
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