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arXiv · 2510.17607

Boundary Depth and Deformations of Symplectic Cohomology

Yoel Groman
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Abstract

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 $SC^*_{\theta}(D)$ 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.

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Yoel Groman. 2025-10-20. Boundary Depth and Deformations of Symplectic Cohomology. https://arxiv.org/abs/2510.17607

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