Polyfold fundamental classes and globally structured multivalued perturbations

Fuente: arXiv
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Autori principali: McDuff, Dusa, Wehrheim, Katrin
Natura: Preprint
Pubblicazione: 2024
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author McDuff, Dusa
Wehrheim, Katrin
author_facet McDuff, Dusa
Wehrheim, Katrin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_15176
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Polyfold fundamental classes and globally structured multivalued perturbations
McDuff, Dusa
Wehrheim, Katrin
Symplectic Geometry
Functional Analysis
46, 53, 58
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.
title Polyfold fundamental classes and globally structured multivalued perturbations
topic Symplectic Geometry
Functional Analysis
46, 53, 58
url https://arxiv.org/abs/2406.15176