Solvable fundamental groups of compact 3-manifolds

Evans, Benny; Moser, Louise

doi:10.1090/S0002-9947-1972-0301742-6

Solvable fundamental groups of compact $3$-manifolds
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by Benny Evans and Louise Moser PDF

Trans. Amer. Math. Soc. 168 (1972), 189-210 Request permission

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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