Notes on differentiable stacks. (English) Zbl 1098.14501

Heinloth, J.

Tschinkel, Yuri (ed.), Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Winter Term 2004/2005. Lecture notes from the seminars “Number theory”, “Algebraic geometry” and “Twisted cohomology theories” held at the University of Göttingen, Göttingen, Germany, 2004. Göttingen: Universitätsdrucke Göttingen (ISBN 3-938616-17-2/pbk). 1-32 (2005).

Summary: We discuss differentiable stacks and their cohomology. We try to give all necessary definitions, avoiding technical machinery as far as possible. In the last section we focus on the example of \(S^1\)-gerbes and explain the relation to projective (Hilbert-)bundles used in a recent paper by D. S. Freed, M. J. Hopkins and C. Teleman [“Twisted \(K\)-theory and loop group representations”, preprint, http://arxiv.org/abs/math/0312155].
For the entire collection see [Zbl 1083.11004].

MSC:

14A20	Generalizations (algebraic spaces, stacks)
19L47	Equivariant \(K\)-theory
19K99	\(K\)-theory and operator algebras