On the stable norm of slit tori and the Farey sequence
Differential Geometry
2023-10-10 v1 Dynamical Systems
Geometric Topology
Abstract
Let (M, g) be a compact manifold endowed with a possibly singular Riemannian metric. The metric induces a norm on the homology of M , called the stable norm. We provide explicit computations of the stable norm of flat slit tori using the Farey sequence. We then glue several slit tori together to produce half-translation surfaces whose unit ball of the stable norm has faces of maximal dimension. Furthermore, we give a sub-quadratic estimate for the asymptotic counting of simple homology classes on these surfaces.
Cite
@article{arxiv.2310.05570,
title = {On the stable norm of slit tori and the Farey sequence},
author = {Pablo Montealegre},
journal= {arXiv preprint arXiv:2310.05570},
year = {2023}
}