Differentiable stacks and gerbes
In this article, which is seen as a continuation of the work ``\(S^1\)-bundles and gerbes over differentiable stacks'' [C. R., Math., Acad. Sci. Paris 336, No. 2, 163--168 (2003; Zbl 1039.58016)] studied by the same authors, the authors present a large background related to differentiable stacks and gerbes. The main purpose of the article is to develop the theory of \(S^1\)-gerbes over differentiable stacks. The work has based on relationship between Lie groupoids and differentiable stacks which has a large application area in different branches of mathematics such as algebraic geometry, differential geometry and differential topology, etc. Specially, the authors show that \(S^1\)-gerbes are in one-to-one correspondence with Morita equivalence classes of groupoid \(S^1\)-central extensions. Also, they show that pseudo-connections can be used to calculate Dixmier-Douady classes. At the end of the work, they give a construction of \(S^1\)-central extensions with the pseudo-curvature.
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