Obstructions to almost complex structures following Massey
Algebraic Topology
2025-11-11 v2 Differential Geometry
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.
Cite
@article{arxiv.2406.05518,
title = {Obstructions to almost complex structures following Massey},
author = {Michael Albanese and Aleksandar Milivojevic},
journal= {arXiv preprint arXiv:2406.05518},
year = {2025}
}
Comments
Improved exposition following referee comments. To appear in Enseign. Math