Homology, Homotopy and Applications

Continuous family groupoids

Alan L. T. Paterson

Full-text: Open access

Abstract

In this paper, we define and investigate the properties of continuous family groupoids. This class of groupoids is necessary for investigating the groupoid index theory arising from the equivariant Atiyah-Singer index theorem for families, and is also required in noncommutative geometry. The class includes that of Lie groupoids, and the paper shows that, like Lie groupoids, continuous family groupoids always admit (an essentially unique) continuous left Haar system of smooth measures. We also show that the action of a continuous family groupoid $G$ on a continuous family $G$-space fibered over another continuous family $G$-space $Y$ can always be regarded as an action of the continuous family groupoid $G*Y$ on an ordinary $G*Y$-space.

Article information

Source
Homology Homotopy Appl., Volume 2, Number 1 (2000), 89-104.

Dates
First available in Project Euclid: 13 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.hha/1139841214

Mathematical Reviews number (MathSciNet)
MR1782594

Zentralblatt MATH identifier
0992.22001

Subjects
Primary: 22A22: Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]
Secondary: 58H05: Pseudogroups and differentiable groupoids [See also 22A22, 22E65]

Citation

Paterson, Alan L. T. Continuous family groupoids. Homology Homotopy Appl. 2 (2000), no. 1, 89--104. https://projecteuclid.org/euclid.hha/1139841214


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