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Homogeneous Spaces, Tits Buildings, and Isoparametric Hypersurfaces
Linus Kramer, Universität Würzburg, Germany
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Memoirs of the American Mathematical Society
2002; 114 pp; softcover
Volume: 158
ISBN-10: 0-8218-2906-8
ISBN-13: 978-0-8218-2906-6
List Price: US$59
Individual Members: US$35.40
Institutional Members: US$47.20
Order Code: MEMO/158/752
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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

  • The Leray-Serre spectral sequence
  • Ranks of homotopy groups
  • Some homogeneous spaces
  • Representations of compact Lie groups
  • The case when \(G\) is simple
  • The case when \(G\) is semisimple
  • Homogeneous compact quadrangles
  • Homogeneous focal manifolds
  • Bibliography
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