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Free Group Actions on Spaces Homotopy Equivalent to a Sphere

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Compositio Mathematica

Abstract

For infinite-dimensional homotopy space forms X/G with G nontrivial finite cyclic groups, we study the homotopy type of X/G. We show that the Euler class of X/G is not zero if and only if X/G is finitely dominated.

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References

  1. Brown, K. S.: Cohomology of Groups, Springer-Verlag, Berlin, 1982, Chap. V.

    Google Scholar 

  2. Cartan, H. and Eilenberg, S.: Homological Algebra, Princeton University Press, Princeton, New Jersey, 1965, Chap. XVI.

    Google Scholar 

  3. Dedecker, P.: Sur la cohomologie non abèlienne: I, Canad. J. Math. 12 (1960), 231-251.

    Google Scholar 

  4. Hasse, H.: Ñber die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952.

    Google Scholar 

  5. Lee, J. B.: Transformation groups on S n + Rm, Topology Appl. 53 (1993), 187-204.

    Google Scholar 

  6. Lavendhomme, R. and Roisin, J. R.: Cohomologie non-abelienne de structures algebriques, J. Algebra 67 (1980), 385-414.

    Google Scholar 

  7. Steenrod, N.: The Topology of Fiber Bundles, Princeton University Press, Princeton, New Jersey, 1951, pp. 151-157.

    Google Scholar 

  8. Wall, C. T. C.: Finiteness conditions for CW-complexes, Ann. of Math. 81 (1965), 56-69.

    Google Scholar 

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Ha, K.Y., Jo, J.H. & Lee, J.B. Free Group Actions on Spaces Homotopy Equivalent to a Sphere. Compositio Mathematica 120, 327–333 (2000). https://doi.org/10.1023/A:1001782700265

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  • DOI: https://doi.org/10.1023/A:1001782700265

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