Reidemeister-type moves for surfaces in four-dimensional space

Volume 42 / 1998

Dennis Roseman Banach Center Publications 42 (1998), 347-380 DOI: 10.4064/-42-1-347-380


We consider smooth knottings of compact (not necessarily orientable) n-dimensional manifolds in $ℝ^{n+2}$ (or $S^{n+2}$), for the cases n=2 or n=3. In a previous paper we have generalized the notion of the Reidemeister moves of classical knot theory. In this paper we examine in more detail the above mentioned dimensions. Examples are given; in particular we examine projections of twist-spun knots. Knot moves are given which demonstrate the triviality of the 1-twist spun trefoil. Another application is a smooth version of a result of Homma and Nagase on a set of moves for regular homotopies of surfaces.


  • Dennis Roseman

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