Betti numbers of Shimura curves and arithmetic three--orbifolds
Differential Geometry
2020-01-08 v1 Number Theory
Abstract
We show that asymptotically the first Betti number, or the arithmetic genus, of a Shimura curve satisfies the Gauss--Bonnet equality. We also show that the first Betti number of a congruence hyperbolic 3--orbifold asymptotically vanishes relatively to hyperbolic volume.
Keywords
Cite
@article{arxiv.1810.10515,
title = {Betti numbers of Shimura curves and arithmetic three--orbifolds},
author = {Mikołaj Frączyk and Jean Raimbault},
journal= {arXiv preprint arXiv:1810.10515},
year = {2020}
}