Continuous fibrations and inverse limits of toposes
The classifying topos of a continuous groupoid. II
Classifying toposes and foliations
For any etale topological groupoid (for example, the holonomy groupoid of a foliation), it is shown that its classifying topos is homotopy equivalent to its classifying space. As an application, we prove that the fundamental group of Haefliger for the (leaf space of) a foliation agrees with the one introduced by Van Est. We also give a new proof of Segal’s theorem on Haefliger’s classifying space .
Presentations of étendues
Deformations of Lie brackets: cohomological aspects
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which “controls” deformations of the structure bracket of the algebroid.
On The Relation Between Connection And Sprays.
Cohomology Theories In Synthetic Differential Geometry.
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