The principal connection contrary to other connections like the affine connection has a tensorial character respect to the principal bundle, does thin mean that if the principal connection is not trivial it follows that the principal bundle isn't trivial either(unlike the case with affine connections and vector bundles)?(adsbygoogle = window.adsbygoogle || []).push({});

If this was the case when constructing a principal bundle starting by its fibre, would the structure of the group bundle(like being abelian or not) obstruct the possible base manifolds in the sense of not being compatible due to topological features like contractibility that automatically make a bundle trivial?

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# A Principal bundle triviality, groups and connections

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