Solvable fundamental groups of compact 3-manifolds

Abstract

A classification is given for groups which can occur as the fundamental group of some compact 3 3 -manifold. In most cases we are able to determine the topological structure of a compact 3 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 3 -manifolds to the more general class of compact 3 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 3 -manifold is a subgroup of the additive group of rationals.

Keywords

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