Symplectic Hodge Theory on Lie Algebroids
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911334027755520 |
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| author | Rankin, Shane |
| author_facet | Rankin, Shane |
| contents | We explore the natural analogues of the Brylinksi condition, Strong Lefschetz condition, and $dδ$-lemma in Symplectic Geometry originally explored by Brylinksi, Mathieu, Yan, and Guillemin in the Symplectic Lie Algebroid case. The equivalence of the three conditions is re-established as a purely algebraic statement along with a primitive notion of the $dδ$-lemma established by Tseng, Yau, and Ho. We then apply this algebraic theory to the desired geometric setting to show that these analogues hold, and finally provide a few classes of examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symplectic Hodge Theory on Lie Algebroids Rankin, Shane Symplectic Geometry Differential Geometry We explore the natural analogues of the Brylinksi condition, Strong Lefschetz condition, and $dδ$-lemma in Symplectic Geometry originally explored by Brylinksi, Mathieu, Yan, and Guillemin in the Symplectic Lie Algebroid case. The equivalence of the three conditions is re-established as a purely algebraic statement along with a primitive notion of the $dδ$-lemma established by Tseng, Yau, and Ho. We then apply this algebraic theory to the desired geometric setting to show that these analogues hold, and finally provide a few classes of examples. |
| title | Symplectic Hodge Theory on Lie Algebroids |
| topic | Symplectic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2411.06012 |