The virtual $\textbf {Z}$-representability of certain $3$-manifold groups
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- by Mark D. Baker
- Proc. Amer. Math. Soc. 103 (1988), 996-998
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947696-8
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Abstract:
We use results on the cohomology of principal congruence subgroups of ${\text {PS}}{{\text {L}}_2}({\mathbf {Z}}[\omega ]),{\omega ^2} + \omega + 1 = 0$, to prove the existence of a large class of closed, orientable $3$-manifolds with virtually ${\mathbf {Z}}$-representable fundamental groups. In particular, these manifolds have finite covers with positive first Betti number.References
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Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 996-998
- MSC: Primary 57M10; Secondary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947696-8
- MathSciNet review: 947696