Invariance of immersed Floer cohomology under Lagrangian surgery
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866918262113042432 |
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| author | Palmer, Joseph Woodward, Chris |
| author_facet | Palmer, Joseph Woodward, Chris |
| contents | We show that Floer cohomology of an immersed Lagrangian brane is invariant under smoothing of a self-intersection point if the quantum valuation of the weakly bounding cochain vanishes and the Lagrangian has dimension at least two. The chain-level map replaces the two orderings of the self-intersection point with meridianal and longitudinal cells on the handle created by the surgery, and uses a bijection between holomorphic disks developed by Fukaya-Oh-Ohta-Ono. Our result generalizes invariance of potentials for certain Lagrangian surfaces in Dimitroglou-Rizell--Ekholm--Tonkonog, and implies the invariance of Floer cohomology under mean curvature flow with this type of surgery, as conjectured by Joyce. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_01943 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Invariance of immersed Floer cohomology under Lagrangian surgery Palmer, Joseph Woodward, Chris Symplectic Geometry 53D40 We show that Floer cohomology of an immersed Lagrangian brane is invariant under smoothing of a self-intersection point if the quantum valuation of the weakly bounding cochain vanishes and the Lagrangian has dimension at least two. The chain-level map replaces the two orderings of the self-intersection point with meridianal and longitudinal cells on the handle created by the surgery, and uses a bijection between holomorphic disks developed by Fukaya-Oh-Ohta-Ono. Our result generalizes invariance of potentials for certain Lagrangian surfaces in Dimitroglou-Rizell--Ekholm--Tonkonog, and implies the invariance of Floer cohomology under mean curvature flow with this type of surgery, as conjectured by Joyce. |
| title | Invariance of immersed Floer cohomology under Lagrangian surgery |
| topic | Symplectic Geometry 53D40 |
| url | https://arxiv.org/abs/1903.01943 |