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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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Keywords: Solvable group, nilpotent group, sufficiently large <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$3$">-manifold, incompressible surface, Seifert fiber space, generalized free product, irreducible <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img11.gif" ALT="$3$">-manifold, nonfinitely generated abelian group
Article copyright: © Copyright 1972 American Mathematical Society