Ambient Isotopy
An ambient isotopy from an embedding of a Manifold 
in 
to another is a Homotopy of selfDiffeomorphisms (or Isomorphisms, or piecewise-linear transformations,etc.) of , starting at the Identity Map, such that the ``last'' Diffeomorphism compounded with the firstembedding of is the second embedding of . In other words, an ambient isotopy is like an Isotopy except thatinstead of distorting the embedding, the whole ambient Space is being stretched and distorted and the embedding isjust ``coming along for the ride.'' For Smooth Manifolds, a Map isIsotopic Iff it is ambiently isotopic.
For Knots, the equivalence of Manifolds under continuous deformation is independent ofthe embedding Space. Knots of opposite Chirality have ambient isotopy, but notRegular Isotopy.
See also Isotopy, Regular Isotopy
References
Hirsch, M. W. Differential Topology. New York: Springer-Verlag, 1988.
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