Titlebook: Cohomology Theory of Topological Transformation Groups; Wu Yi Hsiang Book 1975 Springer-Verlag Berlin Heidelberg 1975 Cohomology.Kohomolog

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Generalities on Compact Lie Groups and ,-Spaces,re necessary for the subsequent development. Basic concepts and definitions will be adequately explained; and proofs of some fundamental theorems will also be included whenever short clear cut proofs are available.

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Structural and Classification Theory of Compact Lie Groups and Their Representations,ometric viewpoint of transformation groups. An explicit and neat understanding of the orbit structure of the adjoint action of a compact Lie group . plays a central role in the classification theory developed by É. Cartan and H. Weyl. This more geometric approach is actually more natural and straigh

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An Equivariant Cohomology Theory Related to Fibre Bundle Theory,e category of .-spaces which . reflects the cohomological behavior of both . and .. Following an idea of A. Borel [cf. B10], we shall define the . of a .-space . to be the . of the . of the . bundle, . → . → ., with the given .-space . as its typical fibre, namely ..

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The Orbit Structure of a ,-Space , and the Ideal Theoretical Invariants of ,(,),ohomology .(.). From the viewpoint of transformation groups, those structures which are usually summarized as the . are certainly the most important geometric structures of a given .. Hence, it is almost imperative to investigate how much of the orbit structure of a given .-space . can actually be d

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The Splitting Principle and the Geometric Weight System of Topological Transformation Groups on Acybserve 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 ., there is a natural induced action

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The Splitting Theorems and the Geometric Weight System of Topological Transformation Groups on Coho groups. From the cohomological point of view, the projective spaces certainly have the simplest, and yet non-trivial, cohomology algebras, namely, truncate polynomial rings. Geometrically, the so-called projective transformation groups which are induced by the linear transformation groups still pro

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