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Immersions with non-zero normal vector fields

Published online by Cambridge University Press:  24 October 2008

Bang-He Li  and
Gui-Song Li
Bang-He Li
Affiliation:
Institute of Systems Science, Academia Sinica, Beijing 100080, China
Gui-Song Li
Affiliation:
Institute of Systems Science, Academia Sinica, Beijing 100080, China
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Extract

Let M be a smooth n-manifold, X be a smooth (2n − 1)-manifold, and g:M → X be a map. It was proved in [6] that g is always homotopic to an immersion. The set of homotopy classes of monomorphisms from TM into g*TX, which is denoted by Sg, may be enumerated either by the method of I. M. James and E. Thomas or by the singularity method of U. Koschorke (see [1] and references therein). When the natural action of π1(XM, g) on Sg is trivial, for example, if X is euclidean, the set Sg is in one-to-one correspondence with the set of regular homotopy classes of immersions homotopic to g (see e.g. [4]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 2 , September 1992 , pp. 281 - 285
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

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