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Annals of Global Analysis and Geometry

, Volume 6, Issue 2, pp 119–140 | Cite as

On a class of compact homogeneous spaces I

  • Alexander Shchetinin
Article

Le K be a compact connected Lie group, L be a connected closed subgroup of K. It is well known that L is a subgroup of maximal rank of K if and only if the Euler characteristic of the manifold M = K/L is positive. Such homogeneous spaces M have been classified in [7, 10]. However, their topological classification was unknown. This classification is obtained in the present article. We show tha two compact homogeneous spaces M = K/L and M′ = K′/L′ of positive Euler characteristic are diffeomorphic if and only if the graded rings H*(M,Z) and H*(M′,Z) are isomorphic. We also obtain the rational homotopy classification of such homogeneous spaces which is not equivalent to the differential one. These results were announced in [15].

Keywords

Present Article Group Theory Homogeneous Space Euler Characteristic Closed Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© VEB Deutscher Verlag der Wissenschaften 1988

Authors and Affiliations

  • Alexander Shchetinin
    • 1
  1. 1.Leningradskii prospektMoskovskii avtomobil'no-doroznyi institytMoskvaUdSSR

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