On Manifold-Like Polyfolds as Differential Geometrical Objects with Applications in Complex Geometry
Abstract
Abstract We argue for more widespread use of manifold-like polyfolds (M-polyfolds) as differential geometric objects. M-polyfolds possess a distinct advantage over differentiable manifolds, enabling a smooth and local change of dimension. To establish their utility, we introduce tensors and prove the existence of Riemannian metrics, symplectic structures, and almost complex structures within the M-polyfold framework. Drawing inspiration from a series of highly acclaimed papers by László Lempert, we are laying the foundation for advancing geometry and function theory in complex M-polyfolds.
Fields of Study & Subjects
Geometric and Algebraic Topology
Computational Geometry and Mesh Generation
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Journal of Geometric Analysis
- Volume
- 36
- Issue
- 7
- Publication date
- 22 May 2026
- Language
- EN