Cohomogeneity one manifolds with singly generated rational cohomology II
Abstract
We classify cohomogeneity one actions on smooth, simply connected, closed manifolds with the rational cohomology of a sphere. In particular, we show that such a manifold is diffeomorphic to a sphere, a Brieskorn variety, the Wu manifold \operatorname{SU}(3)/{\operatorname{SO}}(3) , one of two homogeneous spaces of the form \mathbf{G}_{2}/{\operatorname{SU}}(2) , or a member of a particular four-parameter family of 7 -manifolds.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Geometric and Algebraic Topology
Geometry and complex manifolds
Publication details
- Journal / source
- Documenta Mathematica
- Volume
- 31
- Issue
- 5
- Pages
- 1011–1053
- Publication date
- 4 August 2026
- Language
- EN