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Published in:
2016 | OriginalPaper | Chapter
7. Torsors and Non-abelian \Čech Cohomology
Author : Torsten Wedhorn
Published in: Manifolds, Sheaves, and Cohomology
Publisher: Springer Fachmedien Wiesbaden
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Abstract
Very often one is confronted with construction problems where it is easier to make the construction locally. Then the question arises whether these local constructions ”glue“ to a global object. For instance, on premanifolds it is often easier to construct objects if the premanifold is isomorphic to an open ball in \(\mathbb{K}^{m}\), which is locally always the case. In this chapter we study a general technique to deal with such gluing problems – at least if the difference of two possible local objects is given by a sheaf of groups. For instance two primitives of a \(\mathbb{K}\)-valued function always differ by a locally constant \(\mathbb{K}\)-valued function and these form a sheaf of groups.