Klein bottles in circle bundles
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- by John W. Wood PDF
- Proc. Amer. Math. Soc. 28 (1971), 607-608 Request permission
Abstract:
We prove that the Klein bottle embeds in the total space $E$ of an orientable ${S^1}$-bundle over an orientable $2$-manifold $M$ if and only if $M = {S^2}$ and $E = {S^1} \times {S^2}$ or the lens space $L(4,1)$.References
- Glen E. Bredon and John W. Wood, Non-orientable surfaces in orientable $3$-manifolds, Invent. Math. 7 (1969), 83โ110. MR 246312, DOI 10.1007/BF01389793
- P. J. Hilton and S. Wylie, Homology theory: An introduction to algebraic topology, Cambridge University Press, New York, 1960. MR 0115161
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 607-608
- MSC: Primary 57.20
- DOI: https://doi.org/10.1090/S0002-9939-1971-0278324-2
- MathSciNet review: 0278324