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The equivariant whitehead torsions of equivariant homotopy equivalences between the unit spheres of representations of cyclic groups

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References

  1. S. Araki, Equivariant Whitehead groups and G-expansion categories in Homotopy Theory and Related Topics, Advanced studies in Pure Mathematics 9, Kinokuniya, Tokyo (1987), 1–25.

    Google Scholar 

  2. H. Bass, The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups, Topology 4 (1966), 391–410.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. M. M. Cohen, A course in simple homotopy theory, Graduate Texts in Math. 10, Springer-Verlag, 1973.

    Google Scholar 

  4. T. tom Dieck, Transformation Groups, de Gruyter Studies in Mathematics 8, Berlin; New York; de Gruyter, 1987.

    Google Scholar 

  5. K. H. Dovermann and M. Rothenberg, The Generalized Whitehead Torsion of a G Fibre Homotopy Equivalence, preprint.

    Google Scholar 

  6. H. Hauschild, Äquivariant Whiteheadtorsion, Manuscripta math., 26 (1978), 63–82.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. S. Illman, Whitehead torsion and group actions, Ann. Acad. Sci. Fenn. Ser. AI 588 (1975), 1–44.

    Google Scholar 

  8. S. Illman, Actions of compact Lie groups and the equivariant Whitehead group, Osaka J. Math., 23 (1986), 881–927.

    MathSciNet  MATH  Google Scholar 

  9. S. Illman, A product formula for equivariant Whitehead torsion and geometric applications, Transformation groups, Conf. Proc., Poznań, Lect. Notes In Math. Vol. 1217 (1986), 123–150.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. J. Milnor, Whitehead torsion, Bull, Amer. Math. Soc. 72 (1966), 358–426.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. P. Olum, Self-equivalences of pseudo-projective planes, Topology 4 (1965), 109–127.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. P. Olum, Self-equivalences of pseudo-projective planes II, Topology 10 (1971), 257–260.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. T. Petrie, Pseudo equivalences of G-manifolds, Proc. Symp. Pure Math. 32 (1978), 169–210.

    CrossRef  MathSciNet  Google Scholar 

  14. M. Rothenberg, Torsion invariants and finite transformation groups, Proc. Symp. Pure Math. 32 (1978), 269–311.

    MathSciNet  MATH  Google Scholar 

  15. G. Segal, Equivariant Stable homotopy, Proc. Internat. Congr. Math (Nice, 1970) Gauthiervillars, Paris, 1971, Vol. 2, 59–63.

    Google Scholar 

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© 1989 Springer-Verlag

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Inoue, T. (1989). The equivariant whitehead torsions of equivariant homotopy equivalences between the unit spheres of representations of cyclic groups. In: Kawakubo, K. (eds) Transformation Groups. Lecture Notes in Mathematics, vol 1375. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085603

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  • DOI: https://doi.org/10.1007/BFb0085603

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  • Print ISBN: 978-3-540-51218-9

  • Online ISBN: 978-3-540-46178-4

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