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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On non-orientable surfaces in 4-space which are projected with at most one triple point


Author: Shin Satoh
Journal: Proc. Amer. Math. Soc. 128 (2000), 2789-2793
MSC (1991): Primary 57Q45
Published electronically: March 1, 2000
MathSciNet review: 1652241
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Abstract: We show that if a non-orientable surface embedded in 4-space has a projection into 3-space with at most one triple point, then it is ambient isotopic to a connected sum of some unknotted projective planes and an embedded surface in 4-space with vanishing normal Euler number.


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Additional Information

Shin Satoh
Affiliation: Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka, 558-5858, Japan
Email: susato@sci.osaka-cu.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05310-7
PII: S 0002-9939(00)05310-7
Keywords: Non-orientable surface, connected sum, projective plane, triple point, branch point, normal Euler number
Received by editor(s): July 20, 1998
Received by editor(s) in revised form: October 7, 1998
Published electronically: March 1, 2000
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society