On manifold-like polyfolds as differential geometrical objects with applications in complex geometry
Differential Geometry
2025-03-25 v2 Complex Variables
Symplectic Geometry
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 articles by L\'{a}szl\'{o} Lempert, we lay the foundation for advancing geometry and function theory in complex M-polyfolds.
Cite
@article{arxiv.2401.09875,
title = {On manifold-like polyfolds as differential geometrical objects with applications in complex geometry},
author = {Per Åhag and Rafał Czyż and Håkan Samuelsson Kalm and Aron Persson},
journal= {arXiv preprint arXiv:2401.09875},
year = {2025}
}