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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.''
See also Ambient Isotopy, Regular Isotopy