Spectral equivalence of nearby Lagrangians
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912619236950016 |
|---|---|
| author | Asplund, Johan Deshmukh, Yash Pieloch, Alex |
| author_facet | Asplund, Johan Deshmukh, Yash Pieloch, Alex |
| contents | Let $R$ be a commutative ring spectrum. We construct the wrapped Donaldson--Fukaya category with coefficients in $R$ of any stably polarized Liouville sector. We show that any two $R$-orientable and isomorphic objects admit $R$-orientations so that their $R$-fundamental classes coincide. Our main result is that any closed exact Lagrangian $R$-brane in the cotangent bundle of a closed manifold is isomorphic to an $R$-brane structure on the zero section in the wrapped Donaldson--Fukaya category, generalizing a well-known result over the integers. To achieve this, we prove that the Floer homotopy type of the cotangent fiber is given by the stable homotopy type of the based loop space of the zero section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral equivalence of nearby Lagrangians Asplund, Johan Deshmukh, Yash Pieloch, Alex Symplectic Geometry Algebraic Topology 53D37, 53D12, 55P42 Let $R$ be a commutative ring spectrum. We construct the wrapped Donaldson--Fukaya category with coefficients in $R$ of any stably polarized Liouville sector. We show that any two $R$-orientable and isomorphic objects admit $R$-orientations so that their $R$-fundamental classes coincide. Our main result is that any closed exact Lagrangian $R$-brane in the cotangent bundle of a closed manifold is isomorphic to an $R$-brane structure on the zero section in the wrapped Donaldson--Fukaya category, generalizing a well-known result over the integers. To achieve this, we prove that the Floer homotopy type of the cotangent fiber is given by the stable homotopy type of the based loop space of the zero section. |
| title | Spectral equivalence of nearby Lagrangians |
| topic | Symplectic Geometry Algebraic Topology 53D37, 53D12, 55P42 |
| url | https://arxiv.org/abs/2411.08841 |