An application of groupoid cohomology

Caroline Series

Vol. 92 (1981), No. 2, 415–432

DOI: 10.2140/pjm.1981.92.415

Abstract

We study the structure of analytic measured groupoids as defined by Mackey. It has been observed by Ramsay that an arbitrary groupoid can be thought of as an equivalence relation on its unit space together with a field of isotropy subgroups.

We construct a cohomology theory for equivalence relations with coefficients in a field of abelian groups, and show that two possible definitions using strict cochains or almost everywhere cochains coincide, and show how using this to reconstruct a groupoid from an equivalence relation and a field of groups.

Mathematical Subject Classification 2000

Primary: 22D40

Secondary: 20L15, 46L05, 46M20

Milestones

Received: 20 November 1977

Published: 1 February 1981