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Torsors and Non-abelian \Čech Cohomology

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Manifolds, Sheaves, and Cohomology

Part of the book series: Springer Studium Mathematik - Master ((SSMM))

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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.

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Correspondence to Torsten Wedhorn .

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Wedhorn, T. (2016). Torsors and Non-abelian \Čech Cohomology. In: Manifolds, Sheaves, and Cohomology. Springer Studium Mathematik - Master. Springer Spektrum, Wiesbaden. https://doi.org/10.1007/978-3-658-10633-1_7

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