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arXiv · 1910.10402

Connections on central extensions, lifting gerbes, and finite-dimensional obstruction vanishing

Indranil Biswas·Markus Upmeier
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Abstract

Given a central extension of Lie groups, we study the classification problem of lifting the structure group together with a given connection. For reductive structure groups we introduce a new connective structure on the lifting gerbe associated to this problem. Our main result classifies all connections on the central extension of a given principal bundle. In particular, we find that admissible connections are in one-to-one correspondence with parallel trivializations of the lifting gerbe. Moreover, we prove a vanishing result for Neeb's obstruction classes for finite-dimensional Lie groups.

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Indranil Biswas, Markus Upmeier. 2019-10-23. Connections on central extensions, lifting gerbes, and finite-dimensional obstruction vanishing. https://arxiv.org/abs/1910.10402

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