Polyfold fundamental classes and globally structured multivalued perturbations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916296478687232 |
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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 |