Tameness conjecture for O(n)\mathcal{O}(n)-geometries

Let an O(n)\mathcal{O}(n)-geometry be a Cartan geometry modelled on the corresponding model, and call it tame according to the source's definition. Tameness conjecture. An O(n)\mathcal{O}(n)-geometry is tame if and only if it is isomorphic to a covering space of the model. The source says that the classification of flat complete or flat tame O(n)\mathcal{O}(n)-geometries is unclear, so this equivalence remains open there.

Sources & referencesView supporting material

Primary source

Benjamin McKay, “Morphisms of Cartan connections”, arXiv:0802.1473 (2010).

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