Abstract
When an arbitraryp-groupG acts on a ℤ n -homologyn-sphereX, it is proved here that the dimension functionn:S(G)→ℤ(S(G) is the set of subgroups ofG), defined byn(H)=dimX H, (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.
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Dotzel, R.M., Hamrick, G.C. p-Group actions on homology spheres. Invent Math 62, 437–442 (1980). https://doi.org/10.1007/BF01394253
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DOI: https://doi.org/10.1007/BF01394253