Boundary Depth and Deformations of Symplectic Cohomology
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911221942321152 |
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| author | Groman, Yoel |
| author_facet | Groman, Yoel |
| contents | We study the relation between two versions of symplectic cohomology associated to a Liouville domain $D$ embedded in a symplectic manifold $M$: the ambient version $SC^*_M(D)$ defined over the Novikov field and depending on the embedding, and the intrinsic version $SC^*_θ(D)$ depending on the choice of a local Liouville form and defined over the ground field. We show that when $D$ has sufficiently small boundary depth, the ambient version can be viewed as a deformation of the intrinsic one. This is achieved by constructing a filtration whose associated graded reproduces the intrinsic theory, and developing quantitative tools to control the deformation. We apply our results to constructing local pieces of the SYZ mirror. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary Depth and Deformations of Symplectic Cohomology Groman, Yoel Symplectic Geometry We study the relation between two versions of symplectic cohomology associated to a Liouville domain $D$ embedded in a symplectic manifold $M$: the ambient version $SC^*_M(D)$ defined over the Novikov field and depending on the embedding, and the intrinsic version $SC^*_θ(D)$ depending on the choice of a local Liouville form and defined over the ground field. We show that when $D$ has sufficiently small boundary depth, the ambient version can be viewed as a deformation of the intrinsic one. This is achieved by constructing a filtration whose associated graded reproduces the intrinsic theory, and developing quantitative tools to control the deformation. We apply our results to constructing local pieces of the SYZ mirror. |
| title | Boundary Depth and Deformations of Symplectic Cohomology |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2510.17607 |