Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

The order of a meridian of a knotted Klein bottle

Author(s): Katsuyuki Yoshikawa
Journal: Proc. Amer. Math. Soc. 126 (1998), 3727-3731.
MSC (1991): Primary 57Q45
MathSciNet review: 1468209
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Abstract: We consider the order of a meridian (of the group) of a Klein bottle smoothly embedded in the -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 , there exists a Klein bottle in $S^{4}$ whose meridian has order .

References:

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[2]: F. Gonz $\acute {\text{a}}$ lez-Acuña, Homomorphisms of knot groups, Ann. of Math. 102 (1975), 373-377. MR 52:576
[3]: S. Kinoshita, On the Alexander polynomial of 2-spheres in a 4-sphere, Ann. of Math. 74 (1961), 518-531. MR 24:A2960
[4]: T. M. Price and D. M. Roseman, Embeddings of the projective plane in four space, preprint.

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