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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月22日

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  • Per Åhag,
  • Rafał Czyż,
  • Håkan Samuelsson Kalm,
  • Aron Persson

摘要

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.