Contractible -manifolds of finite genus at infinity

Author:
E. M. Brown

Journal:
Trans. Amer. Math. Soc. **245** (1978), 503-514

MSC:
Primary 57N10

DOI:
https://doi.org/10.1090/S0002-9947-1978-0511426-2

MathSciNet review:
511426

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1978-0511426-2

Keywords:
Proper map,
proper homotopy equivalence,
proper fundamental group,
end,
eventually end-irreducible,
open 3-manifold

Article copyright:
© Copyright 1978
American Mathematical Society