Extensible positive loops and vanishing of symplectic cohomology
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914710384803840 |
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| author | Cant, Dylan Hedicke, Jakob Kilgore, Eric |
| author_facet | Cant, Dylan Hedicke, Jakob Kilgore, Eric |
| contents | The symplectic cohomology of certain symplectic manifolds $W$ with non-compact ends modelled on the positive symplectization of a compact contact manifold $Y$ is shown to vanish whenever there is a positive loop of contactomorphisms of $Y$ which extends to a loop of Hamiltonian diffeomorphisms of $W$. An open string version of this result is also proved: the wrapped Floer cohomology of a Lagrangian $L$ with ideal Legendrian boundary $Λ$ is shown to vanish if there is a positive loop $Λ_{t}$ based at $Λ$ which extends to an exact loop of Lagrangians based at $L$. Various examples of such loops are considered. Applications include the construction of exotic compactly supported symplectomorphisms and exotic fillings of $Λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18267 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extensible positive loops and vanishing of symplectic cohomology Cant, Dylan Hedicke, Jakob Kilgore, Eric Symplectic Geometry 53D40, 53D35, 55U99 The symplectic cohomology of certain symplectic manifolds $W$ with non-compact ends modelled on the positive symplectization of a compact contact manifold $Y$ is shown to vanish whenever there is a positive loop of contactomorphisms of $Y$ which extends to a loop of Hamiltonian diffeomorphisms of $W$. An open string version of this result is also proved: the wrapped Floer cohomology of a Lagrangian $L$ with ideal Legendrian boundary $Λ$ is shown to vanish if there is a positive loop $Λ_{t}$ based at $Λ$ which extends to an exact loop of Lagrangians based at $L$. Various examples of such loops are considered. Applications include the construction of exotic compactly supported symplectomorphisms and exotic fillings of $Λ$. |
| title | Extensible positive loops and vanishing of symplectic cohomology |
| topic | Symplectic Geometry 53D40, 53D35, 55U99 |
| url | https://arxiv.org/abs/2311.18267 |