Inventiones mathematicae

, Volume 62, Issue 3, pp 437–442

p-Group actions on homology spheres

  • Ronald M. Dotzel
  • Gary C. Hamrick

DOI: 10.1007/BF01394253

Cite this article as:
Dotzel, R.M. & Hamrick, G.C. Invent Math (1980) 62: 437. doi:10.1007/BF01394253


When an arbitraryp-groupG acts on a ℤn-homologyn-sphereX, it is proved here that the dimension functionn:S(G)→ℤ(S(G) is the set of subgroups ofG), defined byn(H)=dimXH, (dim here is cohomological dimension) is realised by a real representation ofG, and that there is an equivariant map fromX to the sphere of this representation. A converse is also established.

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Ronald M. Dotzel
    • 1
  • Gary C. Hamrick
    • 1
  1. 1.Department of MathematicsUniversity of TexasAustinUSA

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