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gerbe
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Definitions of gerbe in various dictionaries:
GERBE - In mathematics, a gerbe (; French: [b]) is a construct in homological algebra and topology. Gerbes were introduced by Jean Giraud (Giraud 1971) follo...
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Keep reading for additional results and analysis below.
| Possible Dictionary Clues |
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| a (wheat) sheaf (now obsolete meaning) |
| something resembling a (wheat) sheaf in appearance |
| an abstract construction in homological algebra and geometry providing a certain type of generalisation for a sheaf |
| A kind of ornamental firework. |
| Gerbe description |
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In mathematics, a gerbe (; French: [b]) is a construct in homological algebra and topology. Gerbes were introduced by Jean Giraud (Giraud 1971) following ideas of Alexandre Grothendieck as a tool for non-commutative cohomology in degree 2. They can be seen as a generalization of principal bundles to the setting of 2-categories. Gerbes provide a convenient, if highly abstract, language for dealing with many types of deformation questions especially in modern algebraic geometry. In addition, special cases of gerbes have been used more recently in differential topology and differential geometry to give alternative descriptions to certain cohomology classes and additional structures attached to them. * "Gerbe" is a French (and archaic English) word that literally means wheat sheaf.* |