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Isotopy of 2-Dimensional Cones

Published online by Cambridge University Press:  20 November 2018

Arthur H. Copeland Jr.
Arthur H. Copeland Jr.*
Affiliation:
Northwestern University
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Knowing the isotopy of cones is a crucial first step in knowing the isotopy of finitely triangulable spaces, for the cones are exactly the stars of vertices. Furthermore, they are the simplest examples of contractible spaces, and the non-triviality of the contractible spaces is one of the distinguishing characteristics of isotopy theory as contrasted with homotopy theory.

The present paper is concerned with the cones over 1-dimensional finitely triangulable spaces. It is clear that homeomorphic spaces have homeomorphic cones, hence cones of the same isotopy type. The surprising result of §2 is that there are very few exceptions to the converse statement. The exceptional isotopy classes of cones all contain cones over spaces that are themselves cones.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 201 - 210
Copyright
Copyright © Canadian Mathematical Society 1966

References

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