The order of a meridian of a knotted Klein bottle
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- by Katsuyuki Yoshikawa PDF
- Proc. Amer. Math. Soc. 126 (1998), 3727-3731 Request permission
Abstract:
We consider the order of a meridian (of the group) of a Klein bottle smoothly embedded in the $4$-sphere $S^{4}$. The order of a meridian of a Klein bottle in $S^{4}$ is a non-negative even integer. Conversely, we prove that, for every non-negative even integer $n$, there exists a Klein bottle in $S^{4}$ whose meridian has order $n$.References
- Jeffrey Boyle, Classifying $1$-handles attached to knotted surfaces, Trans. Amer. Math. Soc. 306 (1988), no. 2, 475–487. MR 933302, DOI 10.1090/S0002-9947-1988-0933302-X
- F. González-Acuña, Homomorphs of knot groups, Ann. of Math. (2) 102 (1975), no. 2, 373–377. MR 379671, DOI 10.2307/1971036
- 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
- T. M. Price and D. M. Roseman, Embeddings of the projective plane in four space, preprint.
Additional Information
- Katsuyuki Yoshikawa
- Affiliation: Faculty of Science, Kwansei Gakuin University, Uegahara Nishinomiya, Hyogo 662-8501, Japan
- Email: yoshikawa@kgupyr.kwansei.ac.jp
- Received by editor(s): April 9, 1997
- Communicated by: Dale Alspach
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3727-3731
- MSC (1991): Primary 57Q45
- DOI: https://doi.org/10.1090/S0002-9939-98-04560-2
- MathSciNet review: 1468209