Obstructions to almost complex structures following Massey
Abstract
We provide proofs of two theorems stated by Massey in 1961, concerning the obstructions to finding complex structures on real vector bundles. In addition, we determine the second obstruction to a complex structure on a rank six orientable real vector bundle. The obstructions are fractional parts of integral Stiefel–Whitney classes, and a fourth of an appropriate combination of Pontryagin, Chern, and Euler classes.
Fields of Study & Subjects
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- L’Enseignement Mathématique
- Volume
- 72
- Issue
- 3
- Pages
- 273–304
- Publication date
- 7 January 2026