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Results tagged with gerbes
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user 3473
"Gerbe" is a construct in homological algebra and topology. They can be seen as a generalization of principal bundles to the setting of 2-categories. "Gerbe" is a French (and archaic English) word that literally means wheat sheaf. Gerbes were introduced by Jean Giraud (Giraud 1971) following ideas of Alexandre Grothendieck as a tool for non-commutative cohomology in degree 2.
14
votes
Why do gerbes live in H^2?
It is basically saying that principal $B\mathbb{C}^\times$-bundles are the same as $\mathbb{C}^\times$-gerbes. …
- 4,519
9
votes
Accepted
Is the first differential Pontryagin class a morphism of stacks?
At least in the case of degree four classes one can alternatively use the theory of multiplicative bundle gerbes. … "
"Multiplicative bundle gerbes with connection"
"String connections and Chern-Simons theory"
"Polyakov-Wiegmann formula and multiplicative gerbes" …
- 4,519
6
votes
Accepted
Are bundle gerbes bundles of algebras?
See my paper with Thomas Nikolaus "Four equivalent versions of non-abelian gerbes". … Summarizing, sections of bundle gerbes do not directly form algebras, but they form Kapranov-Voevodsky 2-vector spaces. …
- 4,519
4
votes
Gerbes and Stacks
Here is one way to see it: gerbes on $M$ form a bigroupoid (= bicategory all of whose morphisms and 2-morphisms are invertible). …
- 4,519
2
votes
Geometric models for 2-gerbes
Bundle $n$-gerbes seem to be what you are looking for.
Bundle gerbes can be defined w.r.t. an open cover (then it is what John Greenwood wrote), but don't have to. … A nice example are basic bundle gerbes over compact Lie groups. …
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