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Isotopy and equivalence of knots in 3-manifolds

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 نشر من قبل JungHwan Park
 تاريخ النشر 2020
  مجال البحث
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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 $S^1times S^2$, we give infinitely many examples of knots whose isotopy classes are changed by the Gluck twist.



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