On non-orientable surfaces in 4-space which are projected with at most one triple point
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- Proc. Amer. Math. Soc. 128 (2000), 2789-2793 Request permission
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
- J. Scott Carter and Masahico Saito, Canceling branch points on projections of surfaces in $4$-space, Proc. Amer. Math. Soc. 116 (1992), no. 1, 229–237. MR 1126191, DOI 10.1090/S0002-9939-1992-1126191-0
- J. Scott Carter and Masahico Saito, Reidemeister moves for surface isotopies and their interpretation as moves to movies, J. Knot Theory Ramifications 2 (1993), no. 3, 251–284. MR 1238875, DOI 10.1142/S0218216593000167
- J. Scott Carter and Masahico Saito, Normal Euler classes of knotted surfaces and triple points on projections, Proc. Amer. Math. Soc. 125 (1997), no. 2, 617–623. MR 1372025, DOI 10.1090/S0002-9939-97-03760-X
- Shin’ichi Kinoshita, On the Alexander polynomials of $2$-spheres in a $4$-sphere, Ann. of Math. (2) 74 (1961), 518–531. MR 133126, DOI 10.2307/1970296
- W. S. Massey, Proof of a conjecture of Whitney, Pacific J. Math. 31 (1969), 143–156. MR 250331
- T. M. Price and D. Roseman, Embeddings of the projective plane in four space, preprint.
- K. Yoshikawa, The order of a meridian of a knotted Klein bottle, preprint.
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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2789-2793
- MSC (1991): Primary 57Q45
- DOI: https://doi.org/10.1090/S0002-9939-00-05310-7
- MathSciNet review: 1652241