On transversality in flag manifolds and linearity of amalgams

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.

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