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The virtual $ Z$-representability of $ 3$-manifolds which admit orientation reversing involutions


Author: Shi Cheng Wang
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
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Abstract: We prove a result which supports the Waldhausen Conjecture, i.e., suppose $ M$ is an irreducible orientable $ 3$-manifold with $ \vert{\pi _1}(M)\vert = \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 [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1990-0977930-9
Article copyright: © Copyright 1990 American Mathematical Society

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