Memoirs of the American Mathematical Society 2002; 114 pp; softcover Volume: 158 ISBN10: 0821829068 ISBN13: 9780821829066 List Price: US$59 Individual Members: US$35.40 Institutional Members: US$47.20 Order Code: MEMO/158/752
 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. Readership Graduate students and research mathematicians interested in geometry. Table of Contents  The LeraySerre 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
