Abstract
If p is an odd prime and F is the fixed point set of a smooth Zp action on Sn or Dn, then F is a smooth manifold with a unitary structure. Conversely; most Zp homology disks or spheres with unitary structures are fixed point sets of smooth Zp actions on Dn or Sn for suitable n. The results of this paper show that an arbitrary oriented mod p homology disk or sphere is the fixed point set of a smooth Zp action on some Z[l/2]-homology disk or sphere. This result is in general the best possible.
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Partially supported by NSF Grants MCS 81-04852 and MCS 83-00669
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Schultz, R. A converse to the P. A. Smith theorem for nonunitary homology spheres. Manuscripta Math 51, 171–199 (1985). https://doi.org/10.1007/BF01168352
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DOI: https://doi.org/10.1007/BF01168352