# Reidemeister-type moves for surfaces in four-dimensional space

Banach Center Publications (1998)

- Volume: 42, Issue: 1, page 347-380
- ISSN: 0137-6934

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topRoseman, Dennis. "Reidemeister-type moves for surfaces in four-dimensional space." Banach Center Publications 42.1 (1998): 347-380. <http://eudml.org/doc/208817>.

@article{Roseman1998,

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.},

author = {Roseman, Dennis},

journal = {Banach Center Publications},

keywords = {knotted 3-manifolds; regular isotopy; twist-spun knots; knot moves; immersions of surfaces; knotted surfaces; Reidemeister move; twist-spun knot; embedding; isotopy; projection},

language = {eng},

number = {1},

pages = {347-380},

title = {Reidemeister-type moves for surfaces in four-dimensional space},

url = {http://eudml.org/doc/208817},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Roseman, Dennis

TI - Reidemeister-type moves for surfaces in four-dimensional space

JO - Banach Center Publications

PY - 1998

VL - 42

IS - 1

SP - 347

EP - 380

AB - 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.

LA - eng

KW - knotted 3-manifolds; regular isotopy; twist-spun knots; knot moves; immersions of surfaces; knotted surfaces; Reidemeister move; twist-spun knot; embedding; isotopy; projection

UR - http://eudml.org/doc/208817

ER -

## References

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