Regular isotopy of a link diagram, an equivalence relation in knot theory
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Ambient isotopy (or h-isotopy), two subsets of a fixed topological space are ambient isotopic if there is a homeomorphism, isotopic to the identity map of the ambient space, which carries one subset to the other
Cerf's theorem states that, provided M is simply-connected and dim(M) ≥ 5, the group of pseudo-isotopy diffeomorphisms of M is connected.