Cohomological induction and uniform measure equivalence
Volume 255 / 2021
Fundamenta Mathematicae 255 (2021), 19-49
MSC: 20F65, 22D05, 57M07, 20J06, 57T10.
DOI: 10.4064/fm778-2-2021
Published online: 23 March 2021
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, implies that the graded cohomology algebras 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.
