Elementary moves for higher dimensional knots

Volume 184 / 2004

Dennis Roseman Fundamenta Mathematicae 184 (2004), 291-310 MSC: 57R40, 57R45, 57R52. DOI: 10.4064/fm184-0-16

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.

Authors

  • Dennis RosemanThe University of Iowa
    Iowa City, IA 52242, U.S.A.
    e-mail

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