The limit sets of subgroups of lattices in $PSL(2,R)^r$

TL;DR

This paper characterizes the possible limit sets of finitely generated subgroups within irreducible lattices in the product group PSL(2,R)^r, advancing understanding of their geometric and algebraic structure.

Contribution

It provides a comprehensive description of the limit sets for these subgroups, a novel contribution to the theory of lattices in product groups.

Findings

Classification of limit sets for finitely generated subgroups

Identification of geometric structures of these limit sets

Extension of previous results to higher-rank lattice products

Abstract

In this paper we give a description of the possible limit sets of finitely generated subgroups of irreducible lattices in $PSL(2,R)^r$.