On the Van Est homomorphism for Lie groupoids

  • David Li-Bland

    University of California, Berkeley, USA
  • Eckhard Meinrenken

    University of Toronto, Canada

Abstract

The Van Est homomorphism for a Lie groupoid , as introduced by Weinstein–Xu, is a cochain map from the complex of groupoid cochains to the Chevalley–Eilenberg complex of the Lie algebroid of . It was generalized by Weinstein, Mehta, and Abad-Crainic to a morphism from the Bott–Shulman–Stasheff complex to a (suitably defined) Weil algebra . In this paper, we will give an approach to the Van Est map in terms of the Perturbation Lemma of homological algebra. This approach is used to establish the basic properties of the Van Est map. In particular, we show that on the normalized subcomplex, the Van Est map restricts to an algebra morphism.

Cite this article

David Li-Bland, Eckhard Meinrenken, On the Van Est homomorphism for Lie groupoids. Enseign. Math. 61 (2015), no. 1/2, pp. 93–137

DOI 10.4171/LEM/61-1/2-5