Differentiability Of Integrable Measurable Cocycles Between Nilpotent\n Groups

2015/09/29 by Michael A. Cantrell, Cantrell, Michael · 1 citation
Mathematics · #20E99 #20F65 #28D15 #37A20 #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1509.08966

openalex publication_date 2015/09/29 · openalex created_date 2022/08/14 · openalex updated_date 2026/07/28

Abstract

We prove an analog for integrable measurable cocycles of Pansu's\ndifferentiation theorem for Lipschitz maps between Carnot-Carath 'eodory\nspaces. This yields an alternative, ergodic theoretic proof of Pansu's\nquasi-isometric rigidity theorem for nilpotent groups, answers a question of\nTim Austin regarding integrable measure equivalence between nilpotent groups,\nand gives an independent proof and strengthening of Austin's result that\nintegrable measure equivalent nilpotent groups have bi-Lipschitz asymptotic\ncones. Our main tools are a nilpotent-valued cocycle ergodic theorem and a\nPoincar 'e recurrence lemma for nilpotent groups.\n

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• L^p measure equivalence of nilpotent groups

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