## Seminar on Transformation GroupsThe description for this book, Seminar on Transformation Groups. (AM-46), will be forthcoming. |

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### Contents

COHOMOLOGY MANIFOLDS by A Borel | 1 |

PERIODIC MAPS VIA SMITH THEORY by E E Floyd | 15 |

1 Conservation of Cohomological Local | 67 |

ISOTROPY SUBGROUPS OF TORAL GROUPS | 85 |

FINITENESS OF NUMBER OF ORBIT TYPES | 93 |

SLICES AND EQUIVARIANT MBEDDINGS | 101 |

ORBITS OF HIGHEST DIMENSION by D Montgomery | 117 |

THE SPECTRAL SEQUENCE OF A BIFILTERED MODULE | 133 |

FIXED POINT THEOREMS FOR ELEMENTARY | 157 |

FIXED POINT THEOREMS FOR ELEMENTARY | 173 |

ONE OR WO CLASSES OF ORBITS by A Borel | 185 |

FIXED POINT SETS AND ORBITS OF COMPLEMENTARY | 195 |

23 | 206 |

50 | 216 |

231 | |

REMARKS ON THE SPECTRAL SEQUENCE OF A MAP | 233 |

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### Common terms and phrases

acts trivially acyclic assume assumption Borel bundle closed subgroup closed subset coefficients cohomology manifold cohomology sequence commutative diagram compact connected compact Lie group compact subset component consider contained COROLLARY cross-section defined definition denote differentiable dim H*(X element equivariant equivariant embedding Euclidean G-space exact sequence fibering fibre filtration finite group finite number fixed point set G acts G. D. Mostow group G H-slice hence homology homomorphism implies induces integer isomorphism isotropy groups isotropy subgroups LEMMA Leray sheaf Let f Let G Lie group acting locally compact space Math maximal torus metric module Moreover Mostow natural map notation number of non-conjugate open neighborhood open set orbit types orbits of G orientable p-group p-torsion paracompact Poincare duality prime principal bundle principal orbit PROPOSITION prove rank G REMARK respectively slice spectral sequence subgroup of G topological transformation groups zero

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Page 230 - in generalized manifolds and applications to the theory of transformation groups", to appear. [2] CH Dowker, "Mapping theorems for non-compact spaces", Amer. J. Math.,