isotopy in a sentence

Examples

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