Topology of leaves for minimal laminations by hyperbolic surfaces
Abstract
We construct minimal laminations by hyperbolic surfaces whose generic leaf is a disk and contain any prescribed family of surfaces and with a precise control of the topologies of the surfaces that appear. The laminations are constructed via towers of finite coverings of surfaces for which we need to develop a relative version of residual finiteness which may be of independent interest. The main step in establishing this relative version of residual finiteness is to obtain finite covers with control on the \emph{second systole} of the surface, which is done in the appendix. In a companion paper, the case of other generic leaves is treated.
Keywords
Cite
@article{arxiv.1906.10029,
title = {Topology of leaves for minimal laminations by hyperbolic surfaces},
author = {Sébastien Alvarez and Joaquín Brum and Matilde Martínez and Rafael Potrie},
journal= {arXiv preprint arXiv:1906.10029},
year = {2022}
}
Comments
With an appendix by the authors and Maxime Wolff. 43 pages. 11 figures. Final version. To appear in Journal of Topology