Contractible $3$-manifolds of finite genus at infinity
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- by E. M. Brown PDF
- Trans. Amer. Math. Soc. 245 (1978), 503-514 Request permission
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.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- 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