The order of a meridian of a knotted Klein bottle

Yoshikawa, Katsuyuki

doi:10.1090/S0002-9939-98-04560-2

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 $n$.

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