On transversality in flag manifolds and linearity of amalgams

Sami Douba; Konstantinos Tsouvalas

On transversality in flag manifolds and linearity of amalgams

Group Theory 2026-07-30 v1

Authors: Sami Douba , Konstantinos Tsouvalas

Abstract

We show that the fundamental group of the double of a complete negatively curved locally symmetric manifold along a closed geodesic is linear. More generally, we establish linearity of doubles of torsion-free transverse subgroups (also known in the literature as regular antipodal subgroups) of semisimple Lie groups along biproximal maximal cyclic subgroups.

Keywords

transversality flag manifolds linearity amalgams locally symmetric manifolds semisimple Lie groups

Cite

@article{arxiv.2607.28863,
  title  = {On transversality in flag manifolds and linearity of amalgams},
  author = {Sami Douba and Konstantinos Tsouvalas},
  journal= {arXiv preprint arXiv:2607.28863},
  year   = {2026}
}

Comments

6 pages, comments welcome. Draft submitted to the proceedings of the 40th Summer Conference on Topology and Its Applications, where the first-named author spoke about the related work arXiv:2603.23969