Smooth 2-Group Extensions and Symmetries of Bundle Gerbes

@article{Bunk2020Smooth2E,
  title={Smooth 2-Group Extensions and Symmetries of Bundle Gerbes},
  author={Severin Bunk and Lukas M{\"u}ller and Richard J Szabo},
  journal={Communications in Mathematical Physics},
  year={2020},
  volume={384},
  pages={1829 - 1911}
}
We study bundle gerbes on manifolds M that carry an action of a connected Lie group G. We show that these data give rise to a smooth 2-group extension of G by the smooth 2-group of hermitean line bundles on M. This 2-group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an… 

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