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arXiv · 2007.05796

Isotopy and equivalence of knots in 3-manifolds

Paolo Aceto·Corey Bregman·Christopher W. Davis·JungHwan Park·Arunima Ray
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Abstract

We show that in a prime, closed, oriented 3-manifold M, equivalent knots are isotopic if and only if the orientation preserving mapping class group is trivial. In the case of irreducible, closed, oriented $3$-manifolds we show the more general fact that every orientation preserving homeomorphism which preserves free homotopy classes of loops is isotopic to the identity. In the case of $S^1\times S^2$, we give infinitely many examples of knots whose isotopy classes are changed by the Gluck twist.

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Paolo Aceto, Corey Bregman, Christopher W. Davis, JungHwan Park, Arunima Ray. 2020-07-11. Isotopy and equivalence of knots in 3-manifolds. https://arxiv.org/abs/2007.05796

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