The topology of isoparametric submanifolds
type: Item
instance of: scholarly article
title: The topology of isoparametric submanifolds
zbMATH Open document ID: 0618.57018
author: Richard S. Palais
author: Wu-Yi Hsiang
author: Chuu-Lian Terng
published in: Journal of Differential Geometry
publication date: 1988-01-01T00:00:00Z
review text: It has been known since a famous paper of Bott and Samelson that, using Morse theory, the homology and cohomology of certain homogeneous spaces can be computed algorithmically from Dynkin diagram and multiplicity data. L. Conlon and J. Dadok noted that these spaces are the orbits of the isotropy representations of symmetric spaces. Recently the theory of isoparametric hypersurfaces has been generalized to a theory of isoparametric submanifolds of arbitrary codimension in Euclidean space, and these same orbits turn out to be exactly the homogeneous examples. Even the nonhomogeneous examples have associated to them Weyl groups with Dynkin diagrams marked with multiplicities. We extend and simplify the Bott-Samelson method to compute the homology and cohomology of isoparametric submanifolds from their marked Dynkin diagrams.
Mathematics Subject Classification ID: 57T15
Mathematics Subject Classification ID: 57R19
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 4003085
zbMATH Keywords: Morse theory
zbMATH Keywords: homology and cohomology of isoparametric submanifolds
zbMATH Keywords: marked Dynkin diagrams
zbMATH Keywords: Coxeter group
Wikidata QID: Q104173597
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214442003
OpenAlex ID: W4231380312
DOI: 10.4310/JDG/1214442003
description: scientific article; zbMATH DE number 4003085