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

Paulo Gusmão; Carlos Meniño Cotón

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arXiv · 2206.10970

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

Paulo Gusmão·Carlos Meniño Cotón

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Abstract

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.

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BibTeX RIS

Paulo Gusmão, Carlos Meniño Cotón. 2022-06-22. Leaf topology of minimal hyperbolic foliations with non simply-connected generic leaf. https://arxiv.org/abs/2206.10970

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