Finiteness theorems for congruence reflection groups

TL;DR

This paper explores the effective methods for classifying arithmetic hyperbolic reflection groups, building on previous finiteness results to advance understanding of their structure and classification.

Contribution

It develops an effective approach to classify arithmetic hyperbolic reflection groups, extending prior finiteness theorems with potential applications in group classification.

Findings

Established effective bounds for classification

Extended finiteness results to broader classes

Provided tools for future classification efforts

Abstract

This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible application to the problem of classification of arithmetic hyperbolic reflection groups.