Characteristic classes as complete obstructions

Martina Rovelli

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arXiv · 1610.08893

Characteristic classes as complete obstructions

Martina Rovelli

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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. By plugging in the correct parameters, we recover several classical theorems. 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.

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BibTeX RIS

Martina Rovelli. 2016-10-27. Characteristic classes as complete obstructions. https://arxiv.org/abs/1610.08893

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