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On non-orientable surfaces in 4-space which are projected with at most one triple point
Author(s):
Shin
Satoh
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2789-2793.
MSC (1991):
Primary 57Q45
Posted:
March 1, 2000
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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.
References:
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- -, Reidemeister moves for surface isotopies and their interpretation as moves to movies, J. of Knot Theory and its Ramifications 2 (1993), pp. 251-284. MR 94i:57007
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- -, Normal Euler classes of knotted surfaces and triple points on projections, Proc. of the AMS. 125, No 2 (Feb 1997), pp. 617-623. MR 97d:57030
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- S. Kinoshita, On the Alexander polynomials of 2-spheres in a 4-sphere, Ann. of Math. 74, No 3 (Nov 1961), pp. 518-531. MR 24:A2960
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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:
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
Posted:
March 1, 2000
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2000,
American Mathematical Society
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