Discrete subgroups of the special linear group with thin limit sets

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we construct a discrete Zariski-dense subgroup Γ of SL(n+1,R) whose limit set on Pn is ‘thin’, that is, contained in a CN-smooth curve, for any n ≥ 3 and N > 0. We achieve this by applying the ping-pong lemma to the action of a specially chosen generating set S on the N-th order jet bundle over Pn. We also show that in a sense this is the best possible result: we show that there does not exist any Zariski-dense subgroup Γ ⊆ SL(3,R) whose limit set is contained in a C2-smooth curve, and there does not exist any Zariski-dense subgroup Γ ⊆ SL(n+1,R) whose limit set is contained in a C-smooth curve.

Original languageEnglish
Pages (from-to)365-407
Number of pages43
JournalTransactions of the American Mathematical Society
Volume369
Issue number1
DOIs
StatePublished - 2017

Fingerprint

Dive into the research topics of 'Discrete subgroups of the special linear group with thin limit sets'. Together they form a unique fingerprint.

Cite this