连续族广群胚
Continuous family groupoids
摘要：
本文定义了连续族广群胚，并研究了其性质。这类广群是研究由族的等变Atiyah-Singer指标定理所产生的广群指标理论所必需的，并且在非交换几何中也是必需的。类包括李群胚，并表明，像李群胚，连续家庭群胚总是承认（一个基本上唯一的）连续左哈尔系统的顺利措施。我们还证明了连续族广群$G$在一个连续族$G$ -空间上的作用总是可以看作是连续族广群$Y$在普通$G*Y$ -空间上的作用.
英文摘要：
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.
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