Reidemeister-type moves for surfaces in four-dimensional space

Dennis Roseman

ArticleOriginal scientific text

Title

Reidemeister-type moves for surfaces in four-dimensional space

Authors ¹

Affiliations

The University of Iowa, Iowa City, Iowa, U.S.A.

Abstract

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.

Keywords

ENG

knotted 3-manifolds, regular isotopy, twist-spun knots, knot moves, immersions of surfaces, knotted surfaces

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Title

Reidemeister-type moves for surfaces in four-dimensional space

Affiliations

Abstract

Keywords

Bibliography