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# isotopy

Let $M$ and $N$ be manifolds and $I=[0,1]$ 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 $h_{t}=g_{t}\circ h_{0}$.

Related:

ExampleOfMappingClassGroup, Homeotopy

Type of Math Object:

Definition

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## Mathematics Subject Classification

57R52*no label found*

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