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Maps of Stiefel manifolds and a Borsuk–Ulam theorem

Published online by Cambridge University Press:  20 January 2009

Jan Jaworowski
Jan Jaworowski
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405
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We are concerned with the following classical version of the Borsuk–Ulam theorem: Let f:Sn→Rk be a map and let Af = {x∈Sn|fx= f(−x)}. Then, if k≦n, Af≠φ. In fact, theorems due to Yang [17] give an estimation of the size of Af in terms of the cohomology index. This classical theorem concerns the antipodal action of the group G=ℤ2 on Sn. It has been generalized and extended in many ways (see a comprehensive expository article by Steinlein [16]). This author ([9, 10)] and Nakaoka [14] proved “continuous” or “parameterized” versions of the theorem. Analogous theorems for actions of the groups G=S1 or S3 have been proved in [11], and [12]; compare also [4, 5, 6].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 2 , June 1989 , pp. 271 - 279
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

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