Applications of the Casson-Walker invariant to the knot complement and the cosmetic crossing conjectures

DOI10.1007/S10711-022-00722-6arXiv2103.15277MaRDI QIDQ6363956

Tetsuya Ito

Publication date: 28 March 2021

Abstract: We give a rational surgery formula for the Casson-Walker invariant of a 2-component link in $S^3$ which is a generalization of Matveev-Polyak's formula. As application, we give more examples of non-hyperbolic L-space $M$ such that knots in $M$ are determined by their complements. We also apply the result for the cosmetic crossing conjecture.

Mathematics Subject Classification ID

Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) Knot theory (57K10) Invariants of 3-manifolds (including skein modules, character varieties) (57K31)

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