Isoparametric hypersurfaces with a homogeneous focal manifold

The classification of isoparametric hypersurfaces in spheres with a homogeneous focal manifold is a project that has been started by Linus Kramer. It extends results by E. Cartan and Hsiang and Lawson. Kramer does most part of this classification in his Habilitationsschrift. In particular he obtains a classification for the cases where the homogeneous focal manifold is at least 2-connected. Results of E. Cartan, Dorfmeister and Neher, and Takagi also solve parts of the classification problem. This thesis completes the classification. We classify all closed isoparametric hypersurfaces in spheres with g>2 distinct principal curvatures one of whose multiplicities is 2 such that the lower dimensional focal manifold is homogeneous. The methods are essentially the same as in Kramer's 'Habilitationsschrift'. The cohomology of the focal manifolds in question is known. This leads to two topological classification problems, which are also solved in this thesis. We classify simply connected homogeneous spaces of compact Lie groups with the same integral cohomology ring as a product of spheres S^2 x S^m and m odd on the one hand and a truncated polynomial ring Q[a]/(a^m) with one generator of even degree and m > 1 as its rational cohomology ring on the other hand.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Würzburg

Year

2002

Author dc:creator

• Wolfrom, Martin

Contributors dc:contributor

• Kramer, Linus

Repository record source_url

https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/293

OAI identifier oai:identifier

oai:opus.bibliothek.uni-wuerzburg.de:293