Torus and Z/p actions on manifolds

@article{Sikora2002TorusAZ,
  title={Torus and Z/p actions on manifolds},
  author={Adam S. Sikora},
  journal={Topology},
  year={2002},
  volume={43},
  pages={725-748}
}
  • A. Sikora
  • Published 1 May 2002
  • Mathematics
  • Topology
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6 Citations
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6 Citations

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References

SHOWING 1-10 OF 30 REFERENCES

Poincaré duality in P.A. Smith theory

Let G = S 1 , G = Z=p or more generally G be a nite p- group, where p is an odd prime. If G acts on a space whose cohomology ring fullls Poincar e duality (with appropriate coecients k), we prove a…

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