G-spaces and Fixed Point Sets

@article{Hofmann2000GspacesAF,
  title={G-spaces and Fixed Point Sets},
  author={K. Hofmann and J. Martin},
  journal={Geometriae Dedicata},
  year={2000},
  volume={83},
  pages={39-61}
}
For a compact connected group G, in a compact free G-space M every closed subset is the fixed point set of an autohomeomorphism if the weight of M is not bigger than that of G. In a compact group with nonsingleton components, every closed subset is the fixed point set of an autohomeomorphism if and only if the weight of the whole group is not bigger than that of the component of the identity. 
2 Citations
Fixed Point Theorems

References

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