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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. 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. ==See also== *Regular homotopy *Regular isotopy 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ambient isotopy」の詳細全文を読む スポンサード リンク
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