Invariance of Immersed Floer cohomology under Maslov flows
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866918426713260032 |
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| author | Palmer, Joseph Woodward, Chris Azizi, with an erratum written jointly with Hadi |
| author_facet | Palmer, Joseph Woodward, Chris Azizi, with an erratum written jointly with Hadi |
| contents | We show that immersed Lagrangian Floer cohomology in compact rational symplectic manifolds is invariant under Maslov flows such as coupled mean curvature/Kaehler-Ricci flow in the sense of Smoczyk as a pair of self-intersection points is born or dies at a self-tangency, using results of Ekholm-Etnyre-Sullivan. This proves part of a conjecture of Joyce. We give a lower bound on the time for which the Floer cohomology is invariant under the (forward or backwards) flow, if it exists. This post-publication has an erratum written jointly with Hadi Azizi, which fills in a missing case in the proof Lemma 7.9 (b). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1804_06799 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Invariance of Immersed Floer cohomology under Maslov flows Palmer, Joseph Woodward, Chris Azizi, with an erratum written jointly with Hadi Symplectic Geometry 53D40 We show that immersed Lagrangian Floer cohomology in compact rational symplectic manifolds is invariant under Maslov flows such as coupled mean curvature/Kaehler-Ricci flow in the sense of Smoczyk as a pair of self-intersection points is born or dies at a self-tangency, using results of Ekholm-Etnyre-Sullivan. This proves part of a conjecture of Joyce. We give a lower bound on the time for which the Floer cohomology is invariant under the (forward or backwards) flow, if it exists. This post-publication has an erratum written jointly with Hadi Azizi, which fills in a missing case in the proof Lemma 7.9 (b). |
| title | Invariance of Immersed Floer cohomology under Maslov flows |
| topic | Symplectic Geometry 53D40 |
| url | https://arxiv.org/abs/1804.06799 |