Introduction to the Language of Stacks and Gerbes
@article{Moerdijk2002IntroductionTT, title={Introduction to the Language of Stacks and Gerbes}, author={Ieke Moerdijk}, journal={arXiv: Algebraic Topology}, year={2002} }
This is the text of a series of four one hour lectures given as part of the
“Third Lisbon Summer Lectures in Geometry”, which took place in the
summer of 2002 at the Instituto Tecnico Superior in Lisbon. The lectures
were aimed at an audience consisting of students with some background in
topology (but not necessarily in algebraic geometry). The purpose of the
lectures was to give a quick introduction to gerbes, with an emphasis on
non-abelian ˇCech cohomology.
67 Citations
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References
SHOWING 1-5 OF 5 REFERENCES
Bundle gerbes
- Mathematics
- 1994
Just as C principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral…
On the classification of Regular Lie groupoids
- Mathematics
- 2002
We observe that any regular Lie groupoid G over an manifold M fits
into an extension K → G → E of a foliation groupoid E by a bundle of
connected Lie groups K. If F is the foliation on M given by…
Differential forms in algebraic topology
- MathematicsGraduate texts in mathematics
- 1982
This paper presents a meta-thesis on the basis of a model derived from the model developed in [Bouchut-Boyaval, M3AS (23) 2013] that states that the mode of action of the Higgs boson is determined by the modulus of the E-modulus.