A note on Selberg's Lemma and negatively curved Hadamard manifolds

TL;DR

This paper demonstrates that Selberg's Lemma does not hold for discrete isometry groups acting on negatively curved Hadamard manifolds, answering a question posed by Margulis.

Contribution

It provides a counterexample showing the failure of Selberg's Lemma in the context of negatively curved Hadamard manifolds.

Findings

Selberg's Lemma fails in this setting

Counterexamples for discrete isometry groups

Addresses a question by Margulis

Abstract

Answering a question by Margulis we prove that the conclusion of Selberg's Lemma fails for discrete isometry groups of negatively curved Hadamard manifolds.