Cohomological induction and uniform measure equivalence

2019/04/08 by Gotfredsen, Thomas, Kyed, David · 1 citation
#20F65 #20J06 #22D05 #57M08 #57T10 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1904.03862

Abstract

We construct a general cohomological induction isomorphism from a uniform measure equivalence of locally compact, second countable, unimodular groups which, as a special case, yields that the graded cohomology rings of quasi-isometric, connected, simply connected, nilpotent Lie groups are isomorphic. This unifies results of Shalom and Sauer and also provides new insight into the quasi-isometry classification problem for low dimensional nilpotent Lie groups.

Cited by

• Quantitative polynomial cohomology and applications to \textrm L^p-measure equivalence

Related

• Homological Invariants and Quasi-Isometry
• L^p measure equivalence of nilpotent groups
• Dynamic characterizations of quasi-isometry, and applications to cohomology
• Ergodic maps and the cohomology of nilpotent Lie groups
• On quasi-isometric nilpotent Lie groups