On the real homotopy type of compact complex surfaces
Abstract
We show that on a compact complex surface all Massey products of cohomology classes in degree one vanish beyond length three. Dually, the real Malcev completion of the fundamental group is homogeneously presented by quadratic and cubic relations. In the non-Kähler case, we give an explicit presentation, which is determined by the first Betti number of the surface.
Fields of Study & Subjects
Geometry and complex manifolds
Homotopy and Cohomology in Algebraic Topology
Geometric and Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 5 January 2026
- Document type
- Preprint