Ambient isotopy

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In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an "ambient space", a manifold, taking a submanifold to another submanifold. More precisely, let N and M be manifolds and g and h be embeddings of N in M. The map f, an isotopy of the identity map of M, is defined to be an ambient isotopy taking g to h if f₁g=h.

Consider a manifold M and two submanifolds A and B. An ambient isotopy can be described as a function $H_t(x) \colon M \times[0,1] \to M$ such that $H 0 (x) = id M$ and $\{H_1(a) \colon a \in A\} = B$