nLab
amenable topological groupoid

Context

Higher geometry

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Contents

Definition

(AD-Renault 00) Recalled for instance in (Sims-Williams 12, p. 4).

(ANS 05, def. 1.3)

Properties

Groupoid convolution algebra

Proposition

The groupoid convolution algebra of an amenable topological groupoid is in the bootstrap category.

(Tu 99, prop. 10.7), recalled as (Uuye 11, example 3.6).

Proposition

For an amenable Lie groupoid 𝒢\mathcal{G}, the full groupoid convolution algebra and the reduced one are naturally isomorphic.

This is due to (AD-Renault 00), recalled for instance as (ANS 05, prop. 1.9)

References

  • Aidan Sims, Dana P. Williams, Amenability for Fell bundles over groupoids (arXiv:1201.0792)
  • Johannes Aastrup, Ryszard Nest, Elmar Schrohe, A Continuous Field of C-algebras and the Tangent Groupoid for Manifolds with Boundary_ (arXiv:math/0507317)
  • Jean-Louis Tu, La conjecture de Baum-Connes pour les feuilletages moyennables, K-Theory 17 (1999), no. 3, 215–264. MR 1703305 (2000g:19004) (Portico, subscription needed)

Revised on August 15, 2013 02:05:35 by David Roberts (211.27.208.168)