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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Solvable fundamental groups of compact $ 3$-manifolds


Authors: Benny Evans and Louise Moser
Journal: Trans. Amer. Math. Soc. 168 (1972), 189-210
MSC: Primary 57A65; Secondary 20E40
MathSciNet review: 0301742
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Abstract: A classification is given for groups which can occur as the fundamental group of some compact $ 3$-manifold. In most cases we are able to determine the topological structure of a compact $ 3$-manifold whose fundamental group is known to be solvable. Using the results obtained for solvable groups, we are able to extend some known results concerning nilpotent groups of closed $ 3$-manifolds to the more general class of compact $ 3$-manifolds. In the final section it is shown that each nonfinitely generated abelian group which occurs as a subgroup of the fundamental group of a $ 3$-manifold is a subgroup of the additive group of rationals.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0301742-6
PII: S 0002-9947(1972)0301742-6
Keywords: Solvable group, nilpotent group, sufficiently large $ 3$-manifold, incompressible surface, Seifert fiber space, generalized free product, irreducible $ 3$-manifold, nonfinitely generated abelian group
Article copyright: © Copyright 1972 American Mathematical Society