论文标题
同位素和结中的结与等效性
Isotopy and equivalence of knots in 3-manifolds
论文作者
论文摘要
我们表明，在质量，封闭，定向的3个manifold M中，当等效结是同位素时，并且仅当定向保存映射类组很微不足道时。如果以不可约，封闭，定向$ 3 $ - manifolds，我们表明了一个更一般的事实，即保留免费同质循环类别的每个定向同位素是对身份的同位素。在$ s^1 \ times s^2 $的情况下，我们给出了许多结的示例，其同位素类别通过gluck扭曲而改变。
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.
