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ULC Properties in Neighbourhoods of Embedded Surfaces and Curves in E3

Published online by Cambridge University Press:  20 November 2018

J. W. Cannon
J. W. Cannon*
Affiliation:
The Institute for Advanced Study, Princeton, New Jersey
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In this paper we derive those properties of topologically embedded curves and surfaces in E3 which can be obtained without use of Bing's Side Approximation Theorem [3] for surfaces. The local homology and homotopy properties studied classically play the largest role in the paper, but the final geometrization of some of the results requires theorems such as the PL Schoenflies Theorem, Dehn's Lemma, the Loop Theorem, the Sphere Theorem, and Waldhausen's generalization of the Loop Theorem (n.b., one application of Waldhausen's theorem (in (3.4)) requires use of the nontrivial normal subgroup in the statement of that theorem).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 1 , February 1973 , pp. 31 - 73
Copyright
Copyright © Canadian Mathematical Society 1973

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