Homology, Homotopy and Applications

Continuous family groupoids

Alan L. T. Paterson

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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

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

First available in Project Euclid: 13 February 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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