Explicit formulas for the Hattori–Stong theorem and applications
Abstract
We employ combinatorial techniques to present an explicit formula for the coefficients in front of Chern classes involving in the Hattori-Stong integrability conditions. We also give an evenness condition for the signature of stably almost-complex manifolds in terms of Chern numbers. As an application, it can be showed that the signature of a $2n$-dimensional stably almost-complex manifold whose possibly nonzero Chern numbers being $c_n$ and $c_ic_{n-i}$ is even, which particularly rules out the existence of such structure on rational projective planes. Some other related results and remarks are also discussed in this article.
Fields of Study & Subjects
Matrix Theory and Algorithms
Quantum chaos and dynamical systems
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 2
- Pages
- 735–750
- Publication date
- 11 February 2026
- Language
- EN