The Collaborative International Dictionary
Gerbe \Gerbe\, n. [F., prop. a sheaf.] (Pyrotechny)
A kind of ornamental firework.
n. 1 (context now obsolete English) A (wheat) sheaf 2 Something resembling a (wheat) sheaf in appearance 3 (context mathematics English) an abstract construction in homological algebra and geometry providing a certain type of generalisation for a sheaf 4 (context pyrotechnics English) A kind of ornamental firework.
In mathematics, a gerbe (; ) is a construct in homological algebra and topology. Gerbes were introduced by Jean Giraud 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.
Gerbe may refer to:
- Gerbe, a village in the Aínsa-Sobrarbe municipality, Aragon
- Gerbe, a manufacturer of hosiery and lingerie founded in 1895
Gerbe, a definition of a construct in algebra
- Bundle gerbe
- Gerbe's Vole (Microtus gerbei), a species of rodent in the family Cricetidae
- Communauté de communes de la Gerbe, a federation of municipalities in the Seine-et-Marne département, France
- La Gerbe, a weekly newspaper of the French collaboration with Nazi Germany during World War II
- Nathan Gerbe, an American ice hockey player
- Zéphirin Gerbe (1810-1890) French naturalist