On the genus of congruence surfaces from maximal orders
Geometric Topology
2019-01-24 v1 Group Theory
Abstract
In this paper, we investigate a question of Breuillard and Reid concerning which genera can be obtained by closed congruence surfaces. Specifically, we study a smaller set of objects, namely the closed congruence surfaces which can be constructed by a maximal order in a quaternion algebra, and show that there is no surface of genus 212 in this class. In particular, we show that Breuillard and Reid's question restricted to such surfaces has a negative answer.
Cite
@article{arxiv.1901.07934,
title = {On the genus of congruence surfaces from maximal orders},
author = {Eric Albers and Nicholas Miller},
journal= {arXiv preprint arXiv:1901.07934},
year = {2019}
}