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