The canonical lamination calibrated by a cohomology class
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909992283537408 |
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| author | Backus, Aidan |
| author_facet | Backus, Aidan |
| contents | Let $M$ be a closed oriented Riemannian manifold of dimension $2 \leq d \leq 7$, and let $ρ\in H^{d - 1}(M, \mathbb R)$ have unit norm. We construct a lamination $λ_ρ$ whose leaves are exactly the minimal hypersurfaces which are calibrated by every calibration in $ρ$. The geometry of $λ_ρ$ is closely related to the the geometry of the unit ball of the stable norm on $H_{d - 1}(M, \mathbb R)$, and so we deduce several results constraining the geometry of the stable norm ball in terms of the topology of $M$. These results establish a close analogy between the stable norm on $H_{d - 1}(M, \mathbb R)$ and the earthquake norm on the tangent space to Teichmüller space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The canonical lamination calibrated by a cohomology class Backus, Aidan Differential Geometry Geometric Topology primary: 49Q05, secondary: 53C38, 37F34 Let $M$ be a closed oriented Riemannian manifold of dimension $2 \leq d \leq 7$, and let $ρ\in H^{d - 1}(M, \mathbb R)$ have unit norm. We construct a lamination $λ_ρ$ whose leaves are exactly the minimal hypersurfaces which are calibrated by every calibration in $ρ$. The geometry of $λ_ρ$ is closely related to the the geometry of the unit ball of the stable norm on $H_{d - 1}(M, \mathbb R)$, and so we deduce several results constraining the geometry of the stable norm ball in terms of the topology of $M$. These results establish a close analogy between the stable norm on $H_{d - 1}(M, \mathbb R)$ and the earthquake norm on the tangent space to Teichmüller space. |
| title | The canonical lamination calibrated by a cohomology class |
| topic | Differential Geometry Geometric Topology primary: 49Q05, secondary: 53C38, 37F34 |
| url | https://arxiv.org/abs/2412.00255 |