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Non-simplicially collapsible triangulations of In

Published online by Cambridge University Press:  24 October 2008

Richard E. Goodrick
Richard E. Goodrick
Affiliation:
University of Utah
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Extract

Given any triangulation of a topological n-cell, In, there is an integer k such that the kth barycentric subdivision of the triangulation is simplicially collapsible (3). In the following, we show that given any integer k, we can construct a triangulation of an n-cell, n > 2, whose kth barycentric subdivision is not simplicially collapsible.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 31 - 36
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Bing, R. H. Some aspects of the topology of 3-manifolds related to the Poincaré conjecture. Lectures on modern mathematics, Saaty, T. L., Editor (Published by John Wiley and Sons, Inc., 1964).Google Scholar
(2)Crowell, R. H. and Fox, R. M.Introduction to Knot Theory (Ginn and Co., 1963).Google Scholar
(3)Zeeman, E. C.Seminar on Combinatorial Topology, Mimeographed Notes, Inst. Hautes Études Sci. (Paris, 1963).Google Scholar