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. For example in
knot theory, one considers two
knots the same if one can distort one knot into the other without breaking it. Such a distortion is an example of an ambient isotopy. More precisely, let
N and
M be manifolds and
g and
h be
embeddings of
N in
M. A
continuous map
is defined to be an ambient isotopy taking
g to
h if
F0 is the
identity map, each map
Ft is a
homeomorphism from
M to itself, and
F1 °
g =
h. This implies that the
orientation must be preserved by ambient isotopies. For example, two knots which are
mirror images of each other are in general not equivalent.