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The Eta Invariant and the Connective K-Theory of the Classifying Space for Cyclic 2 Groups

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Abstract

We use the eta invariant to study the connective K-theory groups ko m (Bℤ ℓ ) of the classifying space for the cyclic group ℤℓ where ℓ - 2ν ≥ 2.

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References

  1. Atiyah, M. F.: K-Theory, W. A. Benjamin, New York, 1967.

    Google Scholar 

  2. Atiyah, M. F., Patodi, V. K. and Singer, I. M.: Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Phil. Soc. 77 (1975), 43–69.

    Google Scholar 

  3. Bahri, A., Bendersky, M., Davis, D. and Gilkey, P.: The complex bordism of groups with periodic cohomology, Trans. Amer. Math. Soc. 316 (1989), 673–687.

    Google Scholar 

  4. Barrera-Yanez, E.: The eta invariant, equivariant bordism, connective K theory and manifolds with positive scalar curvature, Ph.D. Thesis, University of Oregon, 1997.

  5. Botvinnik, B. and Gilkey, P.: The Gromov-Lawson-Rosenberg conjecture: The twisted case, Houston J. Math. 23 (1997), 143–160.

    Google Scholar 

  6. Botvinnik, B., Gilkey, P. and Stolz, S.: The Gromov-Lawson-Rosenberg conjecture for groups with periodic cohomology, J. Differential Geom. 46 (1997), 374–405.

    Google Scholar 

  7. Donnelly, H.: Eta invariants for G spaces, Indiana Univ. Math. J. 27 (1978), 889–918.

    Google Scholar 

  8. Gilkey, P.: The eta invariant and the K theory of odd dimensional spherical space forms, Invent. Math. 76 (1984), 421–453.

    Google Scholar 

  9. Gilkey, P.: The Geometry of Spherical Space Form Groups, Series in Pure Math. 7, World Scientific, Singapore, 1989.

    Google Scholar 

  10. Gilkey, P. and Karoubi, M.: K theory for spherical space forms, Topology Appl. 25 (1987), 179–184.

    Google Scholar 

  11. Hashimoto, S.: On the connective K homology groups of the classifying spaces B Z/p 4, Publ. Res. Inst. Math. Sci. 19 (1983), 765–771.

    Google Scholar 

  12. Kobayashi, T., Murakami, S. and Sugawara, M.: Note on J groups of lens spaces, Hiroshima Math. J. 7 (1977), 387–407.

    Google Scholar 

  13. Kobayashi, T. and Sugawara, M.: Note on K O rings of lens spaces mod 2r, Hiroshima Math. J. 8 (1978), 85–90.

    Google Scholar 

  14. Lichnerowicz, A.: Spineurs harmoniques, C.R. Acad. Sci. Paris 257 (1963), 7–9.

    Google Scholar 

  15. Mahammed, N.: K-theorie des espaces lenticulaires, C.R. Acad. Sci. Paris 272 (1971), 1363–1365.

    Google Scholar 

  16. Mahammed, N., Piccinni, R. and Sutter, U.: Some Applications of Topological K Theory, North-Holland, Amsterdam, 1980.

    Google Scholar 

  17. Stolz, S.: Splitting certain MSpin module spectra, Topology 33 (1994), 159–180.

    Google Scholar 

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Authors and Affiliations

  1. Departamento de Matematicas, CINVESTAV-IPN, Apartado Postal 14-740, 07000, Mexico, D.F. Mexico

    Egidio Barrera-Yanez

  2. Mathematics Department, University of Oregon, Eugene, OR, 97403, U.S.A.

    Peter B. Gilkey

Authors
  1. Egidio Barrera-Yanez
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  2. Peter B. Gilkey
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Barrera-Yanez, E., Gilkey, P.B. The Eta Invariant and the Connective K-Theory of the Classifying Space for Cyclic 2 Groups. Annals of Global Analysis and Geometry 17, 289–299 (1999). https://doi.org/10.1023/A:1006582107737

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