Let M and N be manifolds and I=[0,1] the closed unit interval. A smooth map h:M×IN is called an isotopy if the restrictionPlanetmathPlanetmathPlanetmath map ht:=h(-,t):MN is an embeddingPlanetmathPlanetmath for all tI.

In particular, a diffeotopy is an isotopy.

Remark. Given an isotopy h:M×IN, there exists a diffeotopy g:N×IN such that ht=gth0.

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