Non-orientable surfaces in 4-dimensional space

Yongju Bae; J. Scott Carter; Seonmi Choi; Sera Kim

doi:10.1142/S021821651430002X

Non-orientable surfaces in 4-dimensional space

Yongju Bae
, J. Scott Carter
, Seonmi Choi
, Sera Kim

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

This paper is a survey paper that gives detailed constructions and illustrations of some of the standard examples of non-orientable surfaces that are embedded and immersed in 4-dimensional space. The illustrations depend upon their 3-dimensional projections, and indeed the illustrations here depend upon a further projection into the plane of the page. The concepts used to develop the illustrations will be developed herein.

Original language	English
Article number	1430002
Journal	Journal of Knot Theory and its Ramifications
Volume	23
Issue number	11
DOIs	https://doi.org/10.1142/S021821651430002X
State	Published - 12 Oct 2014

Keywords

4-dimensional space
boy's surface
cross-cap
girl's surface
Klein bottle
mobius band
movie moves
Non-orientable surfaces
projective plane
roman surface
twist spun knots

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10.1142/S021821651430002X

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title = "Non-orientable surfaces in 4-dimensional space",

abstract = "This paper is a survey paper that gives detailed constructions and illustrations of some of the standard examples of non-orientable surfaces that are embedded and immersed in 4-dimensional space. The illustrations depend upon their 3-dimensional projections, and indeed the illustrations here depend upon a further projection into the plane of the page. The concepts used to develop the illustrations will be developed herein.",

keywords = "4-dimensional space, boy's surface, cross-cap, girl's surface, Klein bottle, mobius band, movie moves, Non-orientable surfaces, projective plane, roman surface, twist spun knots",

author = "Yongju Bae and Carter, \{J. Scott\} and Seonmi Choi and Sera Kim",

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AU - Bae, Yongju

AU - Carter, J. Scott

AU - Choi, Seonmi

AU - Kim, Sera

PY - 2014/10/12

Y1 - 2014/10/12

N2 - This paper is a survey paper that gives detailed constructions and illustrations of some of the standard examples of non-orientable surfaces that are embedded and immersed in 4-dimensional space. The illustrations depend upon their 3-dimensional projections, and indeed the illustrations here depend upon a further projection into the plane of the page. The concepts used to develop the illustrations will be developed herein.

AB - This paper is a survey paper that gives detailed constructions and illustrations of some of the standard examples of non-orientable surfaces that are embedded and immersed in 4-dimensional space. The illustrations depend upon their 3-dimensional projections, and indeed the illustrations here depend upon a further projection into the plane of the page. The concepts used to develop the illustrations will be developed herein.

KW - 4-dimensional space

KW - boy's surface

KW - cross-cap

KW - girl's surface

KW - Klein bottle

KW - mobius band

KW - movie moves

KW - Non-orientable surfaces

KW - projective plane

KW - roman surface

KW - twist spun knots

UR - https://www.scopus.com/pages/publications/84929160314

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 11

M1 - 1430002

ER -

Non-orientable surfaces in 4-dimensional space

Abstract

Keywords

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