Lie groupoids, sheaves and cohomology. (English) Zbl 1082.58018

Gutt, Simone (ed.) et al., Poisson geometry, deformation quantisation and group representations. Cambridge: Cambridge University Press (ISBN 0-521-61505-4/pbk). London Mathematical Society Lecture Note Series 323, 145-272 (2005).
The paper under review is an introduction to the theory of Lie groupoids and some of their algebraic invariants. More precisely, in Chapter 2 the authors recall the notion of a Lie groupoid and some of the most important constructions and examples. Associated to any Lie groupoid \(G\), one can introduce the category of equivariant sheaves, as well as its derived category. This is done in Chapter 3 along with the explicit construction of the fundamental groupoid \(\pi _1(G)\) associated to the Lie groupoid \(G\). In Chapter 4 general sheaf cohomology is discussed, while sheaf cohomology with compact supports is discussed in Chapter 5.
For the entire collection see [Zbl 1065.53001].


58H05 Pseudogroups and differentiable groupoids
53D17 Poisson manifolds; Poisson groupoids and algebroids