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arXiv · 2406.15176

Polyfold fundamental classes and globally structured multivalued perturbations

Dusa McDuff·Katrin Wehrheim
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Abstract

Work of Hofer--Wysocki--Zehnder has shown that many spaces of pseudoholomorphic curves that arise when studying symplectic manifolds may be described as the zero set of a polyfold Fredholm section. This framework has many analytic advantages. However the methods they develop to extract useful topological information from it are rather cumbersome. This paper develops a general construction of a finite dimensional space of multivalued perturbations of a polyfold Fredholm section such that almost all elements are regularizing. These perturbation are globally structured and explicitly described, and, in cases where the moduli space has no formal boundary, permit a transparent definition of its (rational Cech) fundamental class.

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Dusa McDuff, Katrin Wehrheim. 2024-06-21. Polyfold fundamental classes and globally structured multivalued perturbations. https://arxiv.org/abs/2406.15176

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