On Manifold-Like Polyfolds as Differential Geometrical Objects with Applications in Complex Geometry
Journal article, 2026
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 L & aacute;szl & oacute; Lempert, we are laying the foundation for advancing geometry and function theory in complex M-polyfolds.
Complex structures
Complex M-polyfolds
Riemannian metrics
Scale Banach spaces
Symplectic structures
Almost complex structures
Sc-holomorphic mappings
K & auml
hler structures
Hermitian metrics
M-polyfolds
Author
Per Ahag
Umeå University
Rafal Czyz
Jagiellonian University in Kraków
Håkan Samuelsson Kalm
Chalmers, Mathematical Sciences, Algebra and geometry
University of Gothenburg
Aron Persson
Umeå University
Uppsala University
Journal of Geometric Analysis
1050-6926 (ISSN)
Vol. 36 7 229Subject Categories (SSIF 2025)
Geometry
DOI
10.1007/s12220-026-02455-4