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

 

Contractible $ 3$-manifolds of finite genus at infinity


Author: E. M. Brown
Journal: Trans. Amer. Math. Soc. 245 (1978), 503-514
MSC: Primary 57N10
MathSciNet review: 511426
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Abstract: A class of contractible open 3-manifolds is defined. It is shown that all contractible open 3-manifolds which can be written as a union of cubes with a bounded number of handles are in this class. It is shown that a proper map between manifolds of this class which induces an isomorphism of proper fundamental groups (e.g. a proper homotopy equivalence) is proper homotopic to a homeomorphism. A naturality condition for homomorphisms of proper fundamental groups is developed. It is shown that a natural homomorphism between the proper fundamental groups of these manifolds is induced by a proper map.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0511426-2
PII: S 0002-9947(1978)0511426-2
Keywords: Proper map, proper homotopy equivalence, proper fundamental group, end, eventually end-irreducible, open 3-manifold
Article copyright: © Copyright 1978 American Mathematical Society