Symplectic maps and hyperKähler moment map geometry
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913273726631936 |
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| author | Rollin, Yann |
| author_facet | Rollin, Yann |
| contents | We obtain a correspondence between the group of symplectic diffeomorphisms of a 4-dimensional real torus and the vanishing locus of a certain hyperKähler moment map. This observation gives rise to a new flow, called the modified moment map flow. The construction can be adapted to the polyhedral setting, for which we prove a Duistermaat type theorem. This paper lays out the ground work for some effective polyhedral symplectic geometry and for a potential Morse-Bott theory, with applications to the topology of the space of symplectic maps of the 4-torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_02679 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Symplectic maps and hyperKähler moment map geometry Rollin, Yann Symplectic Geometry Differential Geometry Primary 53D05, 53D20, Secondary 53D30, 57K17 We obtain a correspondence between the group of symplectic diffeomorphisms of a 4-dimensional real torus and the vanishing locus of a certain hyperKähler moment map. This observation gives rise to a new flow, called the modified moment map flow. The construction can be adapted to the polyhedral setting, for which we prove a Duistermaat type theorem. This paper lays out the ground work for some effective polyhedral symplectic geometry and for a potential Morse-Bott theory, with applications to the topology of the space of symplectic maps of the 4-torus. |
| title | Symplectic maps and hyperKähler moment map geometry |
| topic | Symplectic Geometry Differential Geometry Primary 53D05, 53D20, Secondary 53D30, 57K17 |
| url | https://arxiv.org/abs/2110.02679 |