4 Groupoid Cohomology and Extensions
نویسنده
چکیده
We show that Haefliger's cohomology forétale groupoids, Moore's cohomology for locally compact groups and the Brauer group of a locally compact groupoid are all particular cases of sheaf (oř Cech) cohomology for topological simplicial spaces.
منابع مشابه
Groupoid Cohomology and Extensions
We show that Haefliger’s cohomology for étale groupoids, Moore’s cohomology for locally compact groups and the Brauer group of a locally compact groupoid are all particular cases of sheaf (or Čech) cohomology for topological simplicial spaces.
متن کاملCentral S1-extensions of Symplectic Groupoids and the Poisson Classes
It is shown that a central extension of a Lie groupoid by an Abelian Lie group A has a principal A-bundle structure and the extended Lie groupoid is classified by an Euler esclass. Then we prove that for a symplectic α-connected, αβtransversal or α-simply connected groupoid, there exists at most one central S-extension, the Euler es-class of which corresponds to the Poisson cohomology class of ...
متن کاملExtensions of Lie Brackets
We provide a framework for extensions of Lie algebroids, including non-abelian extensions and Lie algebroids over different bases. Our approach involves Ehresmann connections, which allows straight generalizations of classical constructions. We exhibit a filtration in cohomology and explain the associated spectral sequence. We also give a description of the groupoid integrating an extension in ...
متن کاملOn the classification of Regular Lie groupoids
We observe that any regular Lie groupoid G over an manifold M fits into an extension K → G → E of a foliation groupoid E by a bundle of connected Lie groups K. If F is the foliation on M given by the orbits of E and T is a complete transversal to F , this extension restricts to T , as an extension KT → GT → ET of an étale groupoid ET by a bundle of connected groups KT . We break up the classifi...
متن کاملQ-groupoids and Their Cohomology
We approach Mackenzie’s LA-groupoids from a supergeometric point of view by introducing Q-groupoids. A Q-groupoid is a groupoid object in the category of Q-manifolds, and there is a faithful functor from the category of LA-groupoids to the category of Q-groupoids. Using this approach, we associate to every LA-groupoid a double complex whose cohomology simultaneously generalizes Lie groupoid coh...
متن کامل