# 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 $h_{t}=g_{t}\circ h_{0}$.

Title isotopy Isotopy 2013-03-22 14:52:49 2013-03-22 14:52:49 rspuzio (6075) rspuzio (6075) 5 rspuzio (6075) Definition msc 57R52 ExampleOfMappingClassGroup Homeotopy