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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Three-dimensional manifolds with finitely generated fundamental groups


Author: Robert Messer
Journal: Trans. Amer. Math. Soc. 226 (1977), 119-145
MSC: Primary 57A10
MathSciNet review: 0436149
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0436149-9
PII: S 0002-9947(1977)0436149-9
Article copyright: © Copyright 1977 American Mathematical Society