Leaf topology of minimal hyperbolic foliations with non simply-connected generic leaf

Fuente: arXiv
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Autori principali: Gusmão, Paulo, Cotón, Carlos Meniño
Natura: Preprint
Pubblicazione: 2022
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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