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Non-embedding theorems for Y-spaces

Published online by Cambridge University Press:  24 October 2008

K. H. Mayer  and
R. L. E. Schwarzenberger
K. H. Mayer
Affiliation:
University of Bonn and University of Warwick
R. L. E. Schwarzenberger
Affiliation:
University of Bonn and University of Warwick
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Extract

Let X be a compact differentiable manifold of dimension 2m. A differentiable map from X to euclidean (2m + t)-space is an immersion if its Jacobian has rank 2m at each point of X; it is an embedding if it is also one–one. The existence of such an embedding or immersion implies that the characteristic classes of X satisfy certain integrality conditions; these can be used to obtain lower bounds for the integer t. In a similar way many other geometric properties of X can be deduced from a single integrality theorem involving characteristic classes of various vector bundles over X (see for instance (5)).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 601 - 612
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

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