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Homogeneous Spaces, Tits Buildings, and Isoparametric Hypersurfaces
 
Linus Kramer Universität Würzburg, Würzburg, Germany
Front Cover for Homogeneous Spaces, Tits Buildings, and Isoparametric Hypersurfaces
Available Formats:
Electronic ISBN: 978-1-4704-0345-4
Product Code: MEMO/158/752.E
List Price: $62.00
MAA Member Price: $55.80
AMS Member Price: $37.20
Front Cover for Homogeneous Spaces, Tits Buildings, and Isoparametric Hypersurfaces
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  • Front Cover for Homogeneous Spaces, Tits Buildings, and Isoparametric Hypersurfaces
  • Back Cover for Homogeneous Spaces, Tits Buildings, and Isoparametric Hypersurfaces
Homogeneous Spaces, Tits Buildings, and Isoparametric Hypersurfaces
Linus Kramer Universität Würzburg, Würzburg, Germany
Available Formats:
Electronic ISBN:  978-1-4704-0345-4
Product Code:  MEMO/158/752.E
List Price: $62.00
MAA Member Price: $55.80
AMS Member Price: $37.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1582002; 114 pp
    MSC: Primary 51; 53; Secondary 57;

    We classify 1-connected 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.

    Readership

    Graduate students and research mathematicians interested in geometry.

  • Table of Contents
     
     
    • Chapters
    • 1. The Leray-Serre 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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Volume: 1582002; 114 pp
MSC: Primary 51; 53; Secondary 57;

We classify 1-connected 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.

Readership

Graduate students and research mathematicians interested in geometry.

  • Chapters
  • 1. The Leray-Serre 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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