An ambient isotopy from an embedding of a manifold 
in 
to another is a homotopy of self
diffeomorphisms (or isomorphisms,
or piecewise-linear transformations, etc.) of 
, starting at the identity map,
such that the "last" diffeomorphism
compounded with the first embedding of 
is the second embedding of 
. In other words, an ambient isotopy is like an isotopy
except that instead of distorting the embedding, the whole ambient space
is being stretched and distorted and the embedding is just "coming along for
the ride." For a compact smooth manifold 
and a smooth
manifold 
,
both without boundary, a smooth isotopy
of embeddings of 
in 
extends to an ambient isotopy (Hirsch 1988).
Ambient isotopy depends on the ambient space. A chiral knot in 
is not ambiently isotopic to its mirror image, whereas
every smooth embedding of a circle
in 
is unknotted.
Knots." Math. Intell. 20, 33-48,
Fall 1998.