p-Group actions on homology spheres
- Cite this article as:
- Dotzel, R.M. & Hamrick, G.C. Invent Math (1980) 62: 437. doi:10.1007/BF01394253
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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.