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

Indranil Biswas, Markus Upmeier

Research output: Chapter in Book/Report/Conference proceedingPublished conference contribution

1 Citation (Scopus)


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 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.
Original languageEnglish
Title of host publicationGeometry at the Frontier
Subtitle of host publicationSymmetries and Moduli Spaces of Algebraic Varieties
EditorsPaola Comparin, Eduardo Esteves, Sebastián Reyes-Carocca, Rubí E. Rodríguez, Herbert Lange
PublisherAmerican Mathematical Society
ISBN (Electronic)978-1-4704-6422-6
ISBN (Print)978-1-4704-5327-5
Publication statusPublished - 30 Jul 2021
EventGeometry at the Frontier III - Universidad de La Frontera, Pucón, Chile
Duration: 12 Nov 201816 Nov 2018

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


ConferenceGeometry at the Frontier III

Bibliographical note

The first author is partially supported by a J. C. Bose Fellowship.
The second author thanks the TIFR, Mumbai, for hospitality during 03/2017 and was partially funded by DFG grant UP 85/2-1 of the priority program SPP 2026 Geometry at Infinity.


  • connections
  • gerbes
  • central extensions


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