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A linearity theorem for group actions on spheres with applications to homotopy representations

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Commentarii Mathematici Helvetici

Abstract

LetG be a finite group andX an equivariantZ/|G|-homology sphere. By Smith-theory the fixed point setX H for ap-subgroupH is aZ/p-homology sphere of dimensiond(H).

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References

  1. Bauer, S.,Dimension functions of homotopy representations for compact Lie groups (to appear in “Mathematische Annalen”).

  2. Tom Dieck, T.,Homotopiedarstellungen endlicher Gruppen: Dimensionsfunktionen, Invent. Math.67, 231–252, (1982).

    Article  MathSciNet  Google Scholar 

  3. Tom Dieck, T.,Dimension functions of homotopy representations, Mathematica Gottingensis, Heft31 (1985).

  4. Tom Dieck, T.,Die Picard-Gruppe des Burnside-Ringes einer kompakten Lieschen Gruppe I. Mathematica Gottingensis, Heft46 (1986).

  5. Tom Dieck, T.,The singular set of group actions on homotopy spheres. Arch. Math.43, 551–558 (1984).

    Article  MathSciNet  Google Scholar 

  6. Tom Dieck, T.,The homotopy type of group actions on homotopy spheres. Arch. Math.45, 174–179 (1985).

    Article  MathSciNet  Google Scholar 

  7. Tom Dieck, T.,Transformation Groups and Representation Theory. LNM766, Springer 1979.

  8. Tom Dieck, T. andPetrie, T.,Homotopy representations of finite groups. Publ. Math. I.H.E.S.56, 129–169 (1983).

    Google Scholar 

  9. Dotzel, R. M.,An Artin relation (mod 2) for finite group actions on spheres, Pacif J. Math.114, 335–343 (1984).

    MathSciNet  Google Scholar 

  10. Dotzel, R. M. andHamrick, G.,p-group actions on homology spheres. Invent. Math.62, 437–442 (1981).

    Article  MathSciNet  Google Scholar 

  11. Laitinen, E.,Unstable homotopy theory of homotopy representations, in: LNM1217, 210–248 (1987).

  12. Serre, J.-P.,Linear Representations of Finite Groups. GTM42, Springer (1977).

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Authors and Affiliations

  1. SONDERFORSCHUNGSBEREICH 170: “Geometrie und Analysis” Mathematisches Institut, Bunsenstr, 3-5, D-3400, Göttingen

    Stefan Bauer

  2. Department of Mathematics, University of Chicago, 5734 University Avenue, 60637, Chicago, IL

    Stefan Bauer

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  1. Stefan Bauer
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Bauer, S. A linearity theorem for group actions on spheres with applications to homotopy representations. Commentarii Mathematici Helvetici 64, 167–172 (1989). https://doi.org/10.1007/BF02564667

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  • DOI: https://doi.org/10.1007/BF02564667

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