2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218351This expository paper describes the various methods that have yielded partial results on the conjecture that if n > 2, then no lattice in SL(n,R) has a faithful action on the circle (by homeomorphisms). Topics include amenability, Kazhdan's property (T), bounded cohomology, bounded generation, and the Reeb-Thurston Stability Theorem.This version corrects an error in the proof of the Moore Ergodicity TheoremRepresentation TheoryGroup Theory22E40; 57S25text