The Splitting Principle and the Geometric Weight System of Topological Transformation Groups on Acyclic Cohomology Manifolds or Cohomology Spheres

  • Wu Yi Hsiang
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 85)


In this chapter, we apply the general theorems of Chapter IV to the important testing spaces of acyclic cohomology manifolds and cohomology spheres. Observe that, in the setting of topological transformation groups, there is a simple direct relationship between actions on acyclic cohomology manifolds and actions on cohomology spheres, which can be explained as follows. For a given action on a cohomology sphere X, there is a natural induced action on the cone of X, CI, which is an acyclic cohomology manifold. On the other hand, the restriction of an action on an acyclic manifold X to the complement of a fixed point x (if it exists) gives an action on the cohomology sphere (X - {x}). Hence, one need only treat one case and the corresponding result for the other case will follow automatically. In this chapter, we prefer to state the results for the case of acyclic cohomology manifolds because it is the directly applicable to the study of the local theory.


Maximal Torus Weight System Isotropy Subgroup Principal Orbit Torus Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Wu Yi Hsiang
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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