Classification of Principal Bundles and Lie Groupoids with Prescribed Gauge Group Bundle *

@inproceedings{Kirill2001ClassificationOP,
  title={Classification of Principal Bundles and Lie Groupoids with Prescribed Gauge Group Bundle *},
  author={Kirill and I Scott Mackenzie},
  year={2001}
}
By the gauge group bundle of a principal bundle P(B,G) we mean the Lie group bundle associated to P(B, G) through the conjugacy action of G on itself. Given only B and a Lie group bundle M on B, we ask if there exists P(B, G) with gauge group bundle isomorphic to M and, if so, how they can be described. Using a form of Whitehead’s concept of crossed module, in place of the idea of an ‘abstract kernel’, we find an obstruction class in A*(B,ZG) (G the fibretype of M) whose vanishing gives a… CONTINUE READING

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