Heegaard splittings and a theorem of Livesay
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- by J. H. Rubinstein PDF
- Proc. Amer. Math. Soc. 60 (1976), 317-320 Request permission
Abstract:
Let M be a nonorientable 3-manifold which is double covered by ${S^2} \times I$. We give a short proof of the theorem of Livesay [1] that M is homeomorphic to ${P^2} \times I$ (where ${P^2}$ denotes the projective plane).References
- G. R. Livesay, Involutions with two fixed points on the three-sphere, Ann. of Math. (2) 78 (1963), 582–593. MR 155323, DOI 10.2307/1970543
- C. D. Papakyriakopoulos, On solid tori, Proc. London Math. Soc. (3) 7 (1957), 281–299. MR 87944, DOI 10.1112/plms/s3-7.1.281
- C. D. Papakyriakopoulos, On Dehn’s lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1–26. MR 90053, DOI 10.2307/1970113
- Friedhelm Waldhausen, Heegaard-Zerlegungen der $3$-Sphäre, Topology 7 (1968), 195–203 (German). MR 227992, DOI 10.1016/0040-9383(68)90027-X
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 317-320
- MSC: Primary 57A10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0420625-3
- MathSciNet review: 0420625