Affine transverse foliations in sphere bundles
Abstract
Let~$S^{n-1}\rightarrow E \rightarrow M^n$ be an oriented sphere bundle supporting a {smooth} affine transverse foliation. We give a new and elementary proof of the following fact: if the fundamental group {$π_1(M^n)$} is amenable, then the Euler number of the bundle vanishes. As a by-product, we give an upper bound for the Euler number of the bundle in the general case, that is, for non-amenable {$π_1(M^n)$}.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 1 March 2026
- Language
- EN
- Document type
- Preprint