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Results tagged with gerbes
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user 80891
"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.
4
votes
Accepted
Are there any non-trivial $G$-gerbes over the analytic space $\mathbb C$
In fact you have the following general result: Let $G$ be a Lie group, $M$ a manifold, and $p:P\rightarrow M$ a gerbe such that for every open subset $U$ of $M$, the objects of the fibre of $U$ are p …
- 3,652
7
votes
Accepted
References on Gerbes
A reference more accessible, for example for a differential geometer is the chapter 5 of the book of Brylinski which deals only with commutative gerbes. …
- 3,652
2
votes
holonomy of connection on gerbes
$A_{\alpha\beta}=df_{\alpha\beta}+B_\beta-B_\alpha$ implies that
$iA_{\alpha\beta}+iA_{\beta\gamma}+iA_{\gamma\alpha}=$
$i(df_{\alpha\beta}+B_\beta-B_\alpha+df_{\beta\gamma}+B_\gamma-B_\beta+df_{\ga …
- 3,652