Notes on Thin Matrix Groups
Number Theory
2012-12-17 v1 Group Theory
Abstract
These notes were prepared for the MSRI hot topics workshop on superstrong approximation (2012). We give a brief overview of the developments in the theory, especially the fundamental expansion theorem. Applications to diophantine problems on orbits of integer matrix groups, the affine sieve, group theory, gonality of curves and Heegaard genus of hyperbolic three manifolds, are given. We also discuss the ubiquity of thin matrix groups in various contexts, and in particular that of monodromy groups.
Cite
@article{arxiv.1212.3525,
title = {Notes on Thin Matrix Groups},
author = {Peter Sarnak},
journal= {arXiv preprint arXiv:1212.3525},
year = {2012}
}