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Cohomological induction and uniform measure equivalence

Volume 255 / 2021

Thomas Gotfredsen, David Kyed 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.

Authors

  • Thomas GotfredsenDepartment of Mathematics and Computer Science
    University of Southern Denmark
    Campusvej 55
    DK-5230 Odense M, Denmark
    e-mail
  • David KyedDepartment of Mathematics and Computer Science
    University of Southern Denmark
    Campusvej 55
    DK-5230 Odense M, Denmark
    e-mail

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