Cobordism obstructions to complex sections
Abstract
A notion of vector field cobordism for oriented manifolds was defined by Bökstedt and Svane. We extend this notion to define complex section cobordism for almost complex manifolds. We then determine the complex section cobordism groups and a relevant cobordism category. We describe an obstruction which tells us when a cobordism class contains a manifold, which can be equipped with $r$ linearly independent complex sections, in terms of the Chern numbers. Finally, we show that this obstruction vanishes for certain multiplicative generators in the complex cobordism ring.
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Homology Homotopy and Applications
- Publisher
- International Press of Boston
- Volume
- 28
- Issue
- 2
- Pages
- 1–17
- Publication date
- 1 January 2026
- Language
- EN