Might mean (unverified): Generalization of manifolds for Fredholm theory.
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  1. polyfold: Wiktionary

Definitions from Wiktionary (polyfold)

noun:  (mathematics) A metrizable space together with an equivalence class of sc-smooth structures.
adjective:  (physics) Having the same total and azimuthal quantum numbers, similar energy values, but different inner quantum numbers.
adjective:  Having multiple parts or aspects.
adjective:  Having multiple folds.

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