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Reidemeister-type moves for surfaces in four-dimensional space. (English) Zbl 0906.57010
Jones, Vaughan F. R. (ed.) et al., Knot theory. Proceedings of the mini-semester, Warsaw, Poland, July 13–August 17, 1995. Warszawa: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 42, 347-380 (1998).
The author considers compact codimension 2 submanifolds of $${\mathbb R}^4$$ and $${\mathbb R}^5$$. In a previous paper he generalized the Reidemeister moves of classical knot theory to higher dimensions, and in the present paper he considers in more detail what happens in dimensions 4 and 5. As applications, knot moves are given which show that the 1-twist-spun trefoil is unknotted and a smooth version of a result of Homma and Nagase on a set of moves for regular homotopies of surfaces is outlined.
For the entire collection see [Zbl 0890.00048].
Reviewer: C.Kearton (Durham)

##### MSC:
 57Q45 Knots and links in high dimensions (PL-topology) (MSC2010) 57R42 Immersions in differential topology 57R52 Isotopy in differential topology 57R40 Embeddings in differential topology
##### Keywords:
Reidemeister move; twist-spun knot; embedding; isotopy; projection
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