Combinatorics of Non-Abelian Gerbes with Connection and Curvature
Attal, Romain
HAL, hal-00011260 / Harvested from HAL
Text on HAL
We give a functorial definition of $G$-gerbes over a simplicial complex when the local symmetry group $G$ is non-Abelian. These combinatorial gerbes are naturally endowed with a connective structure and a curving. This allows us to define a fibered category equipped with a functorial connection over the space of edge-paths. By computing the curvature of the latter on the faces of an infinitesimal 4-simplex, we recover the cocycle identities satisfied by the curvature of this gerbe. The link with $BF$-theories suggests that gerbes provide a framework adapted to the geometric formulation of strongly coupled gauge theories.
Publié le : 2004-07-05
Classification:  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],  [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],  [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT],  [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] 
@article{hal-00011260,
     author = {Attal, Romain},
     title = {Combinatorics of Non-Abelian Gerbes with Connection and Curvature},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00011260}
}

Attal, Romain. Combinatorics of Non-Abelian Gerbes with Connection and Curvature. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00011260/