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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The virtual $ {\bf Z}$-representability of certain $ 3$-manifold groups


Author: Mark D. Baker
Journal: Proc. Amer. Math. Soc. 103 (1988), 996-998
MSC: Primary 57M10; Secondary 57M25
MathSciNet review: 947696
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0947696-8
PII: S 0002-9939(1988)0947696-8
Article copyright: © Copyright 1988 American Mathematical Society