On Manifold-Like Polyfolds as Differential Geometrical Objects with Applications in Complex Geometry
Artikel i vetenskaplig tidskrift, 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
Författare
Per Ahag
Umeå universitet
Rafal Czyz
Uniwersytet Jagiellonski w Krakowie
Håkan Samuelsson Kalm
Chalmers, Matematiska vetenskaper, Algebra och geometri
Göteborgs universitet
Aron Persson
Umeå universitet
Uppsala universitet
Journal of Geometric Analysis
1050-6926 (ISSN)
Vol. 36 7 229Ämneskategorier (SSIF 2025)
Geometri
DOI
10.1007/s12220-026-02455-4