“Ambient isotopy”的意思、由来-开放百科全书

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Ambient isotopy

释义

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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, for example 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 F_t 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.

References

Armstrong, Basic Topology, Springer-Verlag, 1983

2 : Topology|Maps of manifolds

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