Nonarithmetic hyperbolic manifolds and trace rings

TL;DR

This paper provides a sufficient condition for constructing nonarithmetic hyperbolic manifolds using inbreeding, explicitly constructs infinitely many such examples, and estimates their volumes, advancing understanding of hyperbolic geometry.

Contribution

It introduces a new criterion for nonarithmetic hyperbolic manifolds and constructs infinitely many non-commensurable examples with volume estimates.

Findings

Established a sufficient condition for nonarithmetic manifolds

Constructed infinitely many non-commensurable examples

Provided volume estimates for these manifolds

Abstract

We give a sufficient condition on the hyperplanes used in the inbreeding construction of Belolipetsky-Thomson to obtain nonarithmetic manifolds. We construct explicitly infinitely many examples of such manifolds that are pairwise non-commensurable and estimate their volume.