Work

On Manifold-Like Polyfolds as Differential Geometrical Objects with Applications in Complex Geometry

Year: 2026

Type: article

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.

Source: Journal of Geometric Analysis

DOI: 10.1007/s12220-026-02455-4

Authors: Per Åhag, Rafał Czyż, Håkan Samuelsson Kalm, Aron Persson

Institutions: Umeå University, Jagiellonian University, Chalmers University of Technology, University of Gothenburg, Uppsala University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Umeå Universitet