Skip to main content
SpringerLink
Log in

Über projektive Moduln und Endlichkeitshindernisse bei Transformationsgruppen

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

We study projective modules in the category of functors from homogeneous spaces into abelian groups. Such functors have been considered by Bredon [1]. We show that protective functors are determined by a set of ordinary projective modules over suitable group rings. The general notions are applied to give a quick proof for the product formula of the finiteness obstruction for transformation groups. These finiteness obstructions are straightforward extensions of the Swan-Wall obstructions (see e. g. Quinn [7]). They are important in the study of homotopy representations (tom Dieck — Petrie [3], [4]). This work is also related to Rothenberg [8].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literaturverzeichnis

  1. Bredon, G. E.: Equivariant Cohomology Theories. Lecture Notes in Math. 34. Berlin-Heidelberg-New York: Springer 1967

    Google Scholar 

  2. tom Dieck, T.: Transformation Groups and Representation Theory. Lecture Notes in Math. 766. Berlin-Heidelberg-New York: Springer 1979

    Google Scholar 

  3. tom Dieck, T., and T. Petrie: The Homotopy Structure of Finite Group Actions on Spheres. In: Algebraic Topology Waterloo 1978, p. 222–243. Lecture Notes in Math. 741. Berlin-Heidelber-New York: Springer 1979

    Google Scholar 

  4. tom Dieck, T., and T. Petrie: Homotopy Representations of Finite Groups. In preparation

  5. Hauschild, H.: Äquivariante Whiteheadtorsion. Manuscripta math.26, 63–82 (1978)

    Google Scholar 

  6. James, I. M., and G. B. Segal: On Equivariant Homotopy Type. Topology17, 267–272 (1976)

    Google Scholar 

  7. Quinn, I.: Finite Nilpotent Group Actions on Finite Complexes. In: Geometric Applications to Homotopy Theory I. Lecture Notes in Math. 657. Berlin-Heidelberg-New York: Springer 1968

    Google Scholar 

  8. Rothenberg, M.: Torsion Invariants and Finite Transformation Groups. In: Algebraic and Geometric Topology. AMS Proc. of Symp. in Pure Math. 32 Part 1, 267–311 (1978)

  9. Swan, R. G.: Induced Representations and Projective Modules. Ann. of Math.71, 552–578 (1960)

    Google Scholar 

  10. Swan, R. G.: Periodic Resolutions for Finite Groups. Ann of Math.72, 267–291 (1960)

    Google Scholar 

  11. Wall, C. T. C.: Finiteness Conditions for CW-Complexes. Ann of Math,81, 56–69 (1965)

    Google Scholar 

  12. Wall C. T. C.: Finiteness Conditions for CW-Complexes II. Proc. Roy. Soc. Ser. A295, 129–139 (1966)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut, D - 3400, BunsenstraΣe 3-5, Göttingen Bunderepublik Deutschland

    Tammo tom Dieck

Authors
  1. Tammo tom Dieck
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

tom Dieck, T. Über projektive Moduln und Endlichkeitshindernisse bei Transformationsgruppen. Manuscripta Math 34, 135–155 (1981). https://doi.org/10.1007/BF01165533

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01165533

Search

Navigation