21. Isotopy invariance of the linking number is automatically obtained as the degree is invariant under homotopic maps.22. This is not a knot invariant because it is only well-defined up to regular isotopy . 23. The pants decompositions of S ( isotopy classes of maximal systems of disjoint simple closed curves ). 24. A homotope of a Jordan algebra is again a Jordan algebra : isotopy defines an equivalence relation. 25. Regular homotopy for immersions is similar to isotopy of embeddings : they are both restricted types of homotopies. 26. For example, a path between two smooth embeddings is a "'smooth isotopy " '. 27. In the link that is equivalent ( under ambient isotopy ) to finitely many disjoint circles in the plane. 28. An "'isotopy "'is a homotopy for which each of the three maps is a bijection. 29. A classical knot can be considered an ambient isotopy class of embeddings of the circle into a thickened 2-sphere. 30. The curve complex of a surface S is a complex whose vertices are isotopy classes of simple closed curves on S.
