Reeb flows transverse to foliations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866912167520894976 |
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| author | Zung, Jonathan |
| author_facet | Zung, Jonathan |
| contents | Let $\mathcal F$ be a co-oriented $C^2$ foliation on a closed, oriented 3-manifold. We show that $T\mathcal F$ can be perturbed to a contact structure with Reeb flow transverse to $\mathcal F$ if and only if $\mathcal F$ does not support an invariant transverse measure. The resulting Reeb flow has no contractible orbits. This answers a question of Colin and Honda. The main technical tool in our proof is leafwise Brownian motion which we use to construct good transverse measures for $\mathcal F$; this gives a new perspective on the Eliashberg--Thurston theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_01325 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Reeb flows transverse to foliations Zung, Jonathan Geometric Topology Symplectic Geometry 57R30, 57K33 Let $\mathcal F$ be a co-oriented $C^2$ foliation on a closed, oriented 3-manifold. We show that $T\mathcal F$ can be perturbed to a contact structure with Reeb flow transverse to $\mathcal F$ if and only if $\mathcal F$ does not support an invariant transverse measure. The resulting Reeb flow has no contractible orbits. This answers a question of Colin and Honda. The main technical tool in our proof is leafwise Brownian motion which we use to construct good transverse measures for $\mathcal F$; this gives a new perspective on the Eliashberg--Thurston theorem. |
| title | Reeb flows transverse to foliations |
| topic | Geometric Topology Symplectic Geometry 57R30, 57K33 |
| url | https://arxiv.org/abs/2103.01325 |