eBook ISBN:  9781470403454 
Product Code:  MEMO/158/752.E 
List Price:  $62.00 
MAA Member Price:  $55.80 
AMS Member Price:  $37.20 
eBook ISBN:  9781470403454 
Product Code:  MEMO/158/752.E 
List Price:  $62.00 
MAA Member Price:  $55.80 
AMS Member Price:  $37.20 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 158; 2002; 114 ppMSC: Primary 51; 53; Secondary 57
We classify 1connected compact homogeneous spaces which have the same rational cohomology as a product of spheres \(\mathbb{S}^{n_1}\times\mathbb{S}^{n_2}\), with \(3\leq n_1\leq n_2\) and \(n_2\) odd. As an application, we classify compact generalized quadrangles (buildings of type \(C_2)\) which admit a point transitive automorphism group, and isoparametric hypersurfaces which admit a transitive isometry group on one focal manifold.
ReadershipGraduate students and research mathematicians interested in geometry.

Table of Contents

Chapters

1. The LeraySerre spectral sequence

2. Ranks of homotopy groups

3. Some homogeneous spaces

4. Representations of compact Lie groups

5. The case when $G$ is simple

6. The case when $G$ is semisimple

7. Homogeneous compact quadrangles

8. Homogeneous focal manifolds


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We classify 1connected compact homogeneous spaces which have the same rational cohomology as a product of spheres \(\mathbb{S}^{n_1}\times\mathbb{S}^{n_2}\), with \(3\leq n_1\leq n_2\) and \(n_2\) odd. As an application, we classify compact generalized quadrangles (buildings of type \(C_2)\) which admit a point transitive automorphism group, and isoparametric hypersurfaces which admit a transitive isometry group on one focal manifold.
Graduate students and research mathematicians interested in geometry.

Chapters

1. The LeraySerre spectral sequence

2. Ranks of homotopy groups

3. Some homogeneous spaces

4. Representations of compact Lie groups

5. The case when $G$ is simple

6. The case when $G$ is semisimple

7. Homogeneous compact quadrangles

8. Homogeneous focal manifolds