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Balanced orbits for fibre preserving maps of S1 and S3 actions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1217)

Abstract

Let G=S1 or G=S3, and let p : z → X be a bundle with a fibre preserving action of G. Let q : V → Y be a vector space bundle with a fibre preserving action of G. Let f : Z→V be a fibre preserving map. The paper studies the size of the subset Af made up of the orbits over which the average of f is zero. The size of Af depends on the cohomology index of the action on Z and on the type of the action on V which can be described in terms of a Euler number. The result can be viewed as an extension of a continuous version of the Borsuk-Ulam theorem.

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© 1986 Springer-Verlag

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Jaworowski, J. (1986). Balanced orbits for fibre preserving maps of S1 and S3 actions. In: Jackowski, S., Pawałowski, K. (eds) Transformation Groups Poznań 1985. Lecture Notes in Mathematics, vol 1217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072820

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  • DOI: https://doi.org/10.1007/BFb0072820

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16824-9

  • Online ISBN: 978-3-540-47097-7

  • eBook Packages: Springer Book Archive