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General Position Properties That Characterize 3-Manifolds

Published online by Cambridge University Press:  20 November 2018

R. J. Daverman  and
D. Repovš
R. J. Daverman
Affiliation:
Department of Mathematics University of Tennessee Knoxville, Tennessee 37996-1300
D. Repovš
Affiliation:
Department of Mathematics University of Tennessee Knoxville, Tennessee 37996-1300
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Abstract

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This paper defines three simplicial approximation properties for maps of 2-cells and 2-spheres into spaces, each providing homotopical tameness conditions on the approximating images. These are the general position properties used in the two main results. The first shows that a resolvable generalized 3-manifold is a genuine 3- manifold if and only if it has the weakest of these approximation properties as well as a mild 3-dimensional disjoint disks condition known as the Light Map Separation Property. The second shows a resolvable generalized 3-manifold to be a 3-manifold if and only if it satisfies the strongest of these approximation properties.

Keywords

Primary:57N1057N75Secondary:57N1557N6057P0554B05

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 2 , 01 April 1992 , pp. 234 - 251
Copyright
Copyright © Canadian Mathematical Society 1992

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