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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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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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