PlanetMath: isotopy

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isotopy

(Definition)

Let and be manifolds and the closed unit interval. A smooth map $h\colon M\times I\to N$ is called an isotopy if the restriction map $h_t:=h(-,t):M\to N$ is an embedding for all $t\in I$ .

In particular, a diffeotopy is an isotopy.

Remark. Given an isotopy $h\colon M\times I\to N$ , there exists a diffeotopy $g\colon N\times I\to N$ such that $h_t=g_t\circ h_0$ .

"isotopy" is owned by rspuzio. [ owner history (1) ]

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Cross-references: diffeotopy, embedding, map, restriction, smooth map, interval, unit, closed, manifolds
There are 9 references to this entry.

This is version 2 of isotopy, born on 2004-12-11, modified 2006-07-21.
Object id is 6558, canonical name is Isotopy.
Accessed 2664 times total.

Classification:

57R52 (Manifolds and cell complexes :: Differential topology :: Isotopy)

Pending Errata and Addenda

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