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A theorem of Borsuk—Ulam type for Seifert-fibred 3-manifolds

Published online by Cambridge University Press:  24 October 2008

Kenneth Millett  and
Dale Rolfsen
Kenneth Millett
Affiliation:
University of California, Santa Barbara, CA 93106, U.S.A.
Dale Rolfsen
Affiliation:
University of British Columbia, Vancouver, B.C. V6T 1Y4, Canada
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Extract

Let M denote a compact topological 3-manifold, without boundary, foliated by topological circles in the sense of Seifert's gefaserter Räume[8]. This will be called a Seifert structure, or Seifert fibration on M; the leaves of the foliation are called (regular or exceptional) fibres. Our main result is the following theorem, reminiscent of the theorem of Borsuk—Ulam [1] stating that every continuous function from S3 to S2 takes at least one pair of antipodal points to the same value.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 3 , November 1986 , pp. 523 - 532
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

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