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Handle-theory and engulfing

Published online by Cambridge University Press:  24 October 2008

S. Buoncristiano
S. Buoncristiano
Affiliation:
Università di Pisa
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Extract

This paper is concerned with the engulfing of a polyhedron X from one end δ_ W of a cobordism (W, δ_ W, δ+W). In the case where the pair (W, δ_ W) is highly connected this version of Engulfing is dealt with in Rourke and Sanderson (2) by combining the method used in the proof of the h-cobordism theorem (eliminating handles) with a simple procedure involving handle-moves. A handle-move is an ambient isotopy which shrinks a handle H onto a small regular neighbourhood of its fibre D. Thus, if a closed polyhedron misses D, a handle-move can be applied to cause X to slip off H.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 1 , July 1975 , pp. 111 - 116
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Bing, R. H.Radial engulfing. Conference on Topology of Manifolds,Michigan State University 1967.Google Scholar
(2)Rourke, C. P. and Sanderson, B. J.Introduction to piecewise-linear topology (Springer-Verlag, 1972).CrossRefGoogle Scholar
(3)Stallings, T.The piecewise-linear structure of Euclidean space. Proc. Cambridge Philos. Soc. 58 (1962), 481–488.CrossRefGoogle Scholar
(4)Zeeman, E. C.Seminar on combinatorial topology (notes), I.H.E.S. (Paris) and University of Warwick (Coventry), 1963–1966.Google Scholar