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arXiv · 2509.07749

A local generalisation of frame bundles

Jérémie Pierard de Maujouy
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Abstract

Frame bundles equipped with a principal connection have their local structure characterised by a 1-form, called the Cartan connection 1-form, which gathers the principal connection form and the soldering form. We introduce generalised frame bundles as a smooth manifold equipped with a coframe with value in a suitable Lie algebra and which furthermore satisfies a weakened version of the Maurer-Cartan equation. From this structure it is possible to construct a Lie algebra action on the manifold. We study the question of whether it is possible to construct a Lie group action and build a base manifold over which the initial manifold is a frame bundle. We find that generalised frame bundles can have singular underlying manifolds.

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Jérémie Pierard de Maujouy. 2025-09-09. A local generalisation of frame bundles. https://arxiv.org/abs/2509.07749

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