Can lattices in SL(n,R) act on the circle?

2008/11/01 by Dave Witte Morris, Morris, Dave Witte
Mathematics · #22E40 #57S25 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Holomorphic and Operator Theory #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0811.0051

openalex publication_date 2008/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This 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.

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