Cohomological induction and uniform measure equivalence

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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.

Translated title of the contributionCohomological induction and uniform measure equivalence
Original languageEnglish
JournalFundamenta Mathematicae
Volume255
Issue number1
Pages (from-to)19-49
ISSN0016-2736
DOIs
Publication statusPublished - 2021

Keywords

  • Cohomology
  • Locally compact groups
  • Measure equivalence
  • Nilpotent Lie groups
  • Quasi-isometry

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