isotopy

Let $M$ and $N$ be manifolds and $I=[0,1]$ the closed unit interval. A smooth map $h:M\times I\to N$ 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 $h:M\times I\to N$, there exists a diffeotopy $g:N\times I\to N$ such that $h_t=g_t\circ h_0$.

Title	isotopy
Canonical name	Isotopy
Date of creation	2013-03-22 14:52:49
Last modified on	2013-03-22 14:52:49
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	5
Author	rspuzio (6075)
Entry type	Definition
Classification	msc 57R52
Related topic	ExampleOfMappingClassGroup
Related topic	Homeotopy