The Geometry of Loop Spaces III: Isometry Groups of Contact Manifolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866916066895069184 |
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| author | Egi, Satoshi Maeda, Yoshiaki Rosenberg, Steven |
| author_facet | Egi, Satoshi Maeda, Yoshiaki Rosenberg, Steven |
| contents | Let $M_p$ be a circle bundle with first Chern class $p[ω]$ over a closed $4n$-dimensional integral symplectic manifold $\bigl(\overline{M},ω\bigr)$. Equivalently, $M_p$ is a closed contact $(4n+1)$-manifold whose Reeb orbits are all closed and have the same period. For a metric $g$ on $M_p$ compatible with the symplectic structure and the geometry of the circle fiber, we use Wodzicki-Chern-Simons forms on the loop space $LM_p$ to prove that $π_1({\rm Isom}(M_p,g))$ is infinite for ${|p| \gg 0}$. We also give the first high-dimensional examples of nonvanishing Wodzicki-Pontryagin forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_01800 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Geometry of Loop Spaces III: Isometry Groups of Contact Manifolds Egi, Satoshi Maeda, Yoshiaki Rosenberg, Steven Differential Geometry 35S99, 53D05, 53D10, 58D15 Let $M_p$ be a circle bundle with first Chern class $p[ω]$ over a closed $4n$-dimensional integral symplectic manifold $\bigl(\overline{M},ω\bigr)$. Equivalently, $M_p$ is a closed contact $(4n+1)$-manifold whose Reeb orbits are all closed and have the same period. For a metric $g$ on $M_p$ compatible with the symplectic structure and the geometry of the circle fiber, we use Wodzicki-Chern-Simons forms on the loop space $LM_p$ to prove that $π_1({\rm Isom}(M_p,g))$ is infinite for ${|p| \gg 0}$. We also give the first high-dimensional examples of nonvanishing Wodzicki-Pontryagin forms. |
| title | The Geometry of Loop Spaces III: Isometry Groups of Contact Manifolds |
| topic | Differential Geometry 35S99, 53D05, 53D10, 58D15 |
| url | https://arxiv.org/abs/2011.01800 |