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Abstract

For smooth knottings of compact (not necessarily orientable) $n$-dimensional manifolds in ${\mathbb R}^{n+2}$ (or ${\mathbb S}^{n+2}$ ), we generalize the notion of knot moves to higher dimensions. This reproves and generalizes the Reidemeister moves of classical knot theory. We show that for any dimension there is a finite set of elementary isotopies, called moves, so that any isotopy is equivalent to a finite sequence of these moves.