  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.
