Leaf topology of minimal hyperbolic foliations with non simply-connected generic leaf
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917557856894976 |
|---|---|
| author | Gusmão, Paulo Cotón, Carlos Meniño |
| author_facet | Gusmão, Paulo Cotón, Carlos Meniño |
| contents | A noncompact (oriented) surface satisfies the condition $(\star)$ if their isolated ends are ''accumulated by genus''. We show that every surface satisfying this condition is homeomorfic to the leaf of a minimal codimension one foliation on a closed $3$-manifold whose generic leaf is not simply connected. Moreover, the above result is also true for any prescription of a countable family of noncompact surfaces (satisfying $(\star)$): they can coexist in the same minimal codimension one foliation as above. All the given examples are hyperbolic foliations, meaning that they admit a leafwise Riemannian metric of constant negative curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_10970 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Leaf topology of minimal hyperbolic foliations with non simply-connected generic leaf Gusmão, Paulo Cotón, Carlos Meniño Geometric Topology 57R30 A noncompact (oriented) surface satisfies the condition $(\star)$ if their isolated ends are ''accumulated by genus''. We show that every surface satisfying this condition is homeomorfic to the leaf of a minimal codimension one foliation on a closed $3$-manifold whose generic leaf is not simply connected. Moreover, the above result is also true for any prescription of a countable family of noncompact surfaces (satisfying $(\star)$): they can coexist in the same minimal codimension one foliation as above. All the given examples are hyperbolic foliations, meaning that they admit a leafwise Riemannian metric of constant negative curvature. |
| title | Leaf topology of minimal hyperbolic foliations with non simply-connected generic leaf |
| topic | Geometric Topology 57R30 |
| url | https://arxiv.org/abs/2206.10970 |