2017/09/29 by Nhan‐Phu Chung, Chung, Nhan-Phu, Yongle Jiang +1
Mathematics · #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1709.10218
openalex publication_date 2017/09/29 · openalex created_date 2017/10/06 · openalex updated_date 2026/07/28
In this article, we will prove a full topological version of Popa's measurable cocycle superrigidity theorem for full shifts. More precisely, we prove that every Hölder continuous cocycle for the full shifts of every finitely generated group G that has one end, undistorted elements and sub-exponential divergence function is cohomologous to a group homomorphism via a Hölder continuous transfer map if the target group is complete and admits a compatible bi-invariant metric. Using the ideas of Behrstock, Dru\c tu, Mosher, Mozes and Sapir, we show that the class of our acting groups is large including wide groups having undistorted elements and one-ended groups with strong thick of finite orders. As a consequence, irreducible uniform lattices of most of higher rank connected semisimple Lie groups, mapping class groups of g-genus surfaces with p-punches, g≥ 2, p≥ 0, Thompson group, Aut(Fn), Out(Fn), n≥3, certain (2 dimensional)-Coxeter groups, and one-ended right-angled Artin groups are in our class. This partially extends the main result in our previous paper.