English

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

Differential Geometry 2025-11-10 v2

Abstract

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 PGL3(R){\mathrm{PGL}}_3(\mathbb{R}). Using such surgeries we provide examples of flag structures, of both uniformizable and non-uniformizable type.

Keywords

Cite

@article{arxiv.2406.02053,
  title  = {Geometric surgeries of three-dimensional flag structures and non-uniformizable examples},
  author = {Elisha Falbel and Martin Mion-Mouton},
  journal= {arXiv preprint arXiv:2406.02053},
  year   = {2025}
}

Comments

v2: Revision after referee process. To appear in Transactions of the American Mathematical Society. 20 pages

R2 v1 2026-06-28T16:52:32.516Z