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On the orbit structures of SU(n)-actions on manifolds of the type of Euclidean, spherical or projective spaces. (English) Zbl 0644.57020

In his well-known monograph [Cohomology theory of topological transformation groups (1975; Zbl 0429.57011)] the first author has proposed a program for studying the cohomological aspects of group actions which are parallel to those of linear representations. This paper is another development in this direction which solves the basic problem of orbit structure for SU(n)-actions of the title. The main theorems of the paper determine the geometric weight systems, the sets of isotropy subgroups, and the slice representations for SU(n) actions on manifolds whose cohomology rings are mentioned in the title under the condition that the number of orbit types is not greater than p(n)\(\equiv the\) partition function of n. The conclusion that these actions resemble the orthogonal actions from the above point of view is certainly surprising and it is a highly non-trivial contribution to the subject.
Reviewer: A.Assadi

MSC:

57S15 Compact Lie groups of differentiable transformations
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
57S25 Groups acting on specific manifolds
57R91 Equivariant algebraic topology of manifolds

Citations:

Zbl 0429.57011
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References:

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