The virtual $Z$-representability of $3$-manifolds which admit orientation reversing involutions
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- by Shi Cheng Wang PDF
- Proc. Amer. Math. Soc. 110 (1990), 499-503 Request permission
Abstract:
We prove a result which supports the Waldhausen Conjecture, i.e., suppose $M$ is an irreducible orientable $3$-manifold with $|{\pi _1}(M)| = \infty$; if $M$ admits an orientation reversing involution $\tau$, and $M$ has a nontrivial finite cover, then some finite cover $\tilde M$ of $M$ has positive first Betti number.References
- D. B. A. Epstein, Projective planes in $3$-manifolds, Proc. London Math. Soc. (3) 11 (1961), 469–484. MR 152997, DOI 10.1112/plms/s3-11.1.469
- John Hempel, $3$-Manifolds, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976. Ann. of Math. Studies, No. 86. MR 0415619
- John Hempel, Orientation reversing involutions and the first Betti number for finite coverings of $3$-manifolds, Invent. Math. 67 (1982), no. 1, 133–142. MR 664329, DOI 10.1007/BF01393377 —, Virtually Haken $3$-manifolds. Combinatorial methods in topology and algebraic geometry, Contemp. Math. 44 (1985), 149-157.
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 499-503
- MSC: Primary 57N10
- DOI: https://doi.org/10.1090/S0002-9939-1990-0977930-9
- MathSciNet review: 977930