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1

Reidemeister-type moves for surfaces in four-dimensional space

100%

Roseman D.

Banach Center Publications

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1998

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tom 42

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nr 1

347-380

EN

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.

2

Elementary moves for higher dimensional knots

100%

Roseman D.

Fundamenta Mathematicae

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2004

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tom 184

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nr 1

291-310

EN

For smooth knottings of compact (not necessarily orientable) n-dimensional manifolds in $ℝ^{n+2}$ (or $𝕊^{n+2}$), 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.

3

Projections of knots

26%

Roseman D.

Fundamenta Mathematicae

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1975

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tom 89

|

nr 2

99-110

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Banach Center Publications

3 Roseman D.

1 2004

1 1998

1 1975

Reidemeister-type moves for surfaces in four-dimensional space

Elementary moves for higher dimensional knots

Projections of knots