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Some generalizations of the Borsuk–Ulam theorem and applications to realizing homotopy classes by embedded spheres

Published online by Cambridge University Press:  24 October 2008

Roger Fenn
Roger Fenn
Affiliation:
Istituto Matematico, Pisa University of Sussex
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Extract

In this paper, some theorems of the Borsuk-Ulam type (1) are given. One of these can be applied to show that certain homotopy classes in manifolds cannot be realized by embedded spheres. The n-dimensional sphere Sn is the subset of the euclidean space

Rn+l consisting of all points (x1, …,xn+1) satisfying . Let be a piecewise linear (PL) involution on Sn without fixed points.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 2 , September 1973 , pp. 251 - 256
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

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