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Solvable Fundamental Groups of Compact 3-Manifolds

Benny Evans and Louise Moser
Transactions of the American Mathematical Society
Vol. 168 (Jun., 1972), pp. 189-210
DOI: 10.2307/1996169
Stable URL: http://www.jstor.org/stable/1996169
Page Count: 22
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Solvable Fundamental Groups of Compact 3-Manifolds
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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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