Three-dimensional manifolds with finitely generated fundamental groups

Messer, Robert

doi:10.1090/S0002-9947-1977-0436149-9

Three-dimensional manifolds with finitely generated fundamental groups
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Trans. Amer. Math. Soc. 226 (1977), 119-145 Request permission

Abstract:

Recent results of G. P. Scott and T. W. Tucker indicate that a three-dimensional manifold with a finitely generated fundamental group is, in various senses, close to being compact. In this paper the structure of such a manifold M is described in terms of a certain compact, incompressible submanifold of M. This result is used to show that the product of M with the real line is essentially the interior of a compact 4-manifold. Finally, when M is ${P^2}$-irreducible, a necessary and sufficient condition is given for M to be homeomorphic to the complement of a closed subset of the boundary of a compact 3-manifold.

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