A homotopy from one embedding of a manifold in to another such that at every time, it is an embedding. The notion of isotopy is category independent, so notions of topological, piecewise-linear, smooth, isotopy (and so on) exist. When no explicit mention is made, "isotopy" usually means "smooth isotopy."

# Isotopy

## See also

Ambient Isotopy, Regular Isotopy## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Isotopy." From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Isotopy.html