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Characteristic classes as complete obstructions

  • Martina RovelliEmail author
Article

Abstract

In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a priori only on a single fiber of the bundle. Afterwards, we define a family of invariants of principal bundles that detect the number of group reductions that a principal bundle admits. We prove that they fit into a long exact sequence of abelian groups, together with the cohomology of the base space and the cohomology of the classifying space of the structure group.

Keywords

Characteristic class Group reduction Obstruction Principal bundle Classifying space 

Notes

Acknowledgements

This paper is part of my PhD thesis, and I would like to thank my advisor Kathryn Hess for her support and for her constructive feedback on earlier versions of this paper. I am grateful to Jeffrey Carlson for suggesting an alternative description of the plus-cohomology groups, and to Viktoriya Ozornova for many extremely helpful discussions. The quality of exposition benefited from the referee’s comments.

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Copyright information

© Tbilisi Centre for Mathematical Sciences 2019

Authors and Affiliations

  1. 1.Department of MathematicsÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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