The Teichm\"uller space of the Hirsch foliation
Geometric Topology
2015-07-07 v1 Differential Geometry
Dynamical Systems
Abstract
We prove that the Teichm\"uller space of the Hirsch foliation (a minimal foliation of a closed 3-manifold by non-compact hyperbolic surfaces) is homeomorphic to the space of closed curves in the plane. This allows us to show that that the space of hyperbolic metrics on the foliation is a trivial principal fiber bundle. And that the structure group of this bundle, the arc-connected component of the identity in the group of homeomorphisms which are smooth on each leaf and vary continuously in the smooth topology in the transverse direction of the foliation, is contractible.
Keywords
Cite
@article{arxiv.1507.01531,
title = {The Teichm\"uller space of the Hirsch foliation},
author = {Sébastien Alvarez and Pablo Lessa},
journal= {arXiv preprint arXiv:1507.01531},
year = {2015}
}