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Piecewise linear immersions

Published online by Cambridge University Press:  24 October 2008

Anthony Smith
Anthony Smith
Affiliation:
Trinity College, Cambridge
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0. Introduction. An immersion f of one space X in another Y is a continuous map which is locally an embedding; that is, for any x ∈ X there is a neighbourhood N(x) of x such that f|N(x) is an embedding. Thus the image of an immersion may intersect itself, but it can contain no worse singularities. For example, the well-known model of the Klein Bottle is the image of an immersion into ordinary 3-space; the locus of points of self intersection is a circle, where two distinct circles in the Klein Bottle have their images. This paper obtains a sufficient condition for a map of PL manifolds to be deformable into a PL immersion.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 45 - 55
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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