Complex vector fields and a vanishing theorem for the Euler characteristic
Abstract
In this paper, we give a more elegant and systematic proof of Jacobowitz’s theorem which relates complex vector fields and the topology of the underlying manifold. The method we use is due to Atiyah [ Vector fields on manifolds (English, with French and German summaries), Westdeutscher Verlag, Cologne, 1970], who applied it to the study of real vector fields and characteristic numbers.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 5
- Pages
- 2189–2194
- Publication date
- 5 March 2026
- Language
- EN