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On the cobordism groups of immersions and embeddings

Published online by Cambridge University Press:  24 October 2008

András Szücs
András Szücs
Affiliation:
Department of Analysis, Eötvös University, Budapest, Hungary H-1088
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Extract

In the present paper we suggest as a cobordism invariant of an immersed or embedded submanifold in Euclidean space the singularity set of its projection to a hyperplane. A similar approach has been employed by Banchoff[1] and Koschorke[6]; see also [15]. We consider the range of dimensions n ≤ 3k where n is the dimension and k is the codimension. We prove that in this range (1) our singularity invariant is complete modulo 2-torsion, and (2) modulo-torsion, it can take any value from Thorm's oriented cobordism group of corresponding dimension for k even, while for k odd this invariant is always trivial.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 2 , March 1991 , pp. 343 - 349
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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