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Collapsing K × I to vertical segments

Published online by Cambridge University Press:  24 October 2008

Perrin Wright
Perrin Wright
Affiliation:
Florida State University
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Extract

In this paper we shall consider contractible 2-dimensional cell complexes K with one 0-cell v, one l-cell a, and one 2-cell D, where the boundary of D is attached to a by a word in a and a−1. In order for such a complex K to be contractible, the attaching word in a and a−1 must have total degree ± 1. The simplest example occurs when the attaching word is a; in this case K is a 2-cell, and is of no interest since K is collapsible. If any other word of degree ± 1 is used, the resulting K is contractible but not collapsible.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 1 , January 1971 , pp. 71 - 74
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Lickorish, W. B. R.On collapsing X2 × I. Address at Georgia Conference on Topology, 1969.Google Scholar
(2)Zeeman, E. C.On the dunce hat. Topology 2 (1964), 341–358.CrossRefGoogle Scholar