Differential geometry of gerbes

By L. Breen, William Messing. 2001

204 citations recorded by the source corpus.

Abstract We define in a global manner the notion of a connective structure for a gerbe on a space X . When the gerbe is endowed with trivializing data with respect to an open cover of X , we describe this connective structure in two separate ways, which extend from abelian to general gerbes the corresponding descriptions due to J.-L. Brylinski and N. Hitchin. We give a global definition of the 3-curvature of this connective structure as a 3-form on X with values in the Lie stack of the gauge stack of the gerbe. We also study this notion locally in terms of more traditional Lie algebra-valued 3-forms. The Bianchi identity, which the curvature of a connection on a principal bundle satisfies, is replaced here by a more elaborate equation.

Subfields: Algebra and Number Theory, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/352b48fe8129e3444046173308670642cbbde523

How researchers see this paper

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In Algebra and Number Theory

1. Urs Schreiber
2. John C. Baez
3. John Huerta
4. Danny Stevenson
5. B. Noohi
6. A. Henriques
7. Chenchang Zhu
8. Abdenacer Makhlouf

In Mathematical Physics

1. John Huerta
2. John C. Baez
3. Urs Schreiber
4. Danny Stevenson
5. B. Noohi
6. E. Aldrovandi
7. A. Henriques
8. Chenchang Zhu

In Nuclear and High Energy Physics

1. John Huerta
2. John C. Baez
3. Danny Stevenson
4. Urs Schreiber
5. Andreas Gustavsson

Citations in the corpus

• Higher gauge theory (2005, background): “We then show that for a certain class of structure 2-groups, such differential forms reduce to Breen and Messing’s ‘connections on nonabelian gerbes’ [ 18 ].”
• An invitation to higher gauge theory (2010, methodology): “Nonetheless, the quantity F − t(B) plays an important role in Breen and Messing’s formalism: they call it the fake curvature.”
• Butterflies I: Morphisms of 2-group stacks (2008, background): “By Morita theory (see [12], or more precisely a categorification of it) the un-pointed 2-groupoid Hom(TORS(H ), TORS(G )) consists of (H ,G )-bimodules, namely stacks with simultaneous left H and right G -actions, that are actually torsors for the right G -action.”
• Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “, these are bundles with typical fiber being a groupoid, in the case of the fibers being degree 2 Q-manifolds over a point these will be the nonabelian bundle gerbes of [6].”
• The Classifying Space of a Topological 2-Group (2008, background): “These structures show up not only in mathematics, where they form a useful generalization of nonabelian gerbes [8], but also in physics, where they can be used to describe parallel transport of strings [29, 30].”