Abstract
One obtains descriptions of the cohomology ring of the manifolds mentioned in the title in terms of their multiplicities and the Euler, respectively Stiefel–Whitney classes of the curvature distributions. Lifts of equifocal hypersurfaces in symmetric spaces are also discussed.
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Cartan, E.: Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces spheriques, Math. Z. 45 (1939), 335–367.
Ferus, D., Karcher, H. and Münzner, H.-F.: Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z. 177 (1981),479–502.
Greenberg, M. and Harper, J. R.:Algebraic Topology: A First Course, Benjamin, New York, 1981.
Grove, K. and Halperin, S.: Dupin hypersurfaces, group actions and the double mapping cylinder, J. Diff. Geom. 26 (1987), 429–459.
Hsiang, W.-Y., Palais, R. S. and Terng, C.-L.: Topology of isoparametric submanifolds, J. Diff. Geom. 27 (1988), 423–460.
Liao, S. D.: On the theory of obstructions of fiber bundles, Ann. of Math. 60(1) (1954), 146–191.
Mare, A.-L.: Topology of isotropy orbits, Doctoral dissertation, Universität Augsburg, 1998.
Munkres, J. R.: Elements of Algebraic Topology, Benjamin, New York, 1984.
Münzner, H. F.: Isoparametrische Hyperflächen in Sphären I, Math. Ann. 251 (1980), 57–71.
Münzner, H. F.: Isoparametrische Hyperflächen in Sphären II, Math. Ann. 256 (1981), 215–232.
Palais, R. S. and Terng, C.-L.: Critical Point Theory and Submanifold Geometry, Springer-Verlag, 1989.
Steenrod, M.: Topology of Fiber Bundles, Princeton Univ. Press, 1951.
Terng, C.-L.: Proper Fredholm submanifolds of Hilbert space, J. Diff. Geom. 29 (1989), 9–47.
Terng, C.-L. and Thorbergsson, G.: Submanifold geometry in symmetric spaces, J. Diff. Geom. 42 (1995), 665–718.
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Mare, AL. Cohomology of Isoparametric Hypersurfaces in Hilbert Space. Geometriae Dedicata 85, 21–43 (2001). https://doi.org/10.1023/A:1010336521152
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DOI: https://doi.org/10.1023/A:1010336521152