Cohomogeneity one manifolds with singly generated rational cohomology II
Jason DeVito

TL;DR
This paper classifies smooth, simply connected manifolds with the rational cohomology of a sphere that admit cohomogeneity one actions, identifying specific geometric and topological types such manifolds can have.
Contribution
It provides a complete classification of such manifolds with cohomogeneity one actions, including explicit descriptions of their diffeomorphism types.
Findings
Manifolds are diffeomorphic to spheres, Brieskorn varieties, Wu manifold, or specific homogeneous spaces.
Identifies a four-parameter family of 7-manifolds with these properties.
Classifies all cohomogeneity one actions on these manifolds.
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 , one of two homogeneous spaces of the form ,or a member of a particular four-parameter family of -manifolds.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Geometry and complex manifolds
