On the eta invariant of (2,3,5) distributions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915258882326528 |
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| author | Haller, Stefan |
| author_facet | Haller, Stefan |
| contents | We consider the Rumin complex associated with a generic rank two distribution on a closed 5-manifold. The Rumin differential in middle degrees gives rise to a self-adjoint differential operator of Heisenberg order two. We study the eta function and the eta invariant of said operator, twisted by unitary flat vector bundles. For (2,3,5) nilmanifolds this eta invariant vanishes but the eta function is nontrivial, in general. We establish a formula expressing the eta function of (2,3,5) nilmanifolds in terms of more elementary functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_18417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the eta invariant of (2,3,5) distributions Haller, Stefan Differential Geometry Representation Theory Spectral Theory 58J28 (primary) and 11M35, 11M41, 53C17, 58A30, 58J10, 58J42 We consider the Rumin complex associated with a generic rank two distribution on a closed 5-manifold. The Rumin differential in middle degrees gives rise to a self-adjoint differential operator of Heisenberg order two. We study the eta function and the eta invariant of said operator, twisted by unitary flat vector bundles. For (2,3,5) nilmanifolds this eta invariant vanishes but the eta function is nontrivial, in general. We establish a formula expressing the eta function of (2,3,5) nilmanifolds in terms of more elementary functions. |
| title | On the eta invariant of (2,3,5) distributions |
| topic | Differential Geometry Representation Theory Spectral Theory 58J28 (primary) and 11M35, 11M41, 53C17, 58A30, 58J10, 58J42 |
| url | https://arxiv.org/abs/2504.18417 |