Geometric surgeries of three-dimensional flag structures and non-uniformizable examples

In this paper, we introduce a notion of geometric surgery for flag structures, which are geometric structures locally modelled on the three-dimensional flag space under the action of ${\mathrm{P}\mathrm{G}\mathrm{L}}_3(\mathbb{R})$. Using such surgeries we provide examples of flag structures, of both uniformizable and non-uniformizable type.