English

Hitchin grafting representations I: Geometry

Differential Geometry 2025-07-03 v2 Geometric Topology

Abstract

We give a geometric interpretation of Fock--Goncharov positivity and show that bending deformations of Fuchsian representations stabilize a uniform Finsler quasi-convex disk in the symmetric space PSLd(R)/PSO(d)\mathrm{PSL}_d(\mathbb R)/\mathrm{PSO}(d).

Cite

@article{arxiv.2506.23392,
  title  = {Hitchin grafting representations I: Geometry},
  author = {Pierre-Louis Blayac and Ursula Hamenstädt and Théo Marty},
  journal= {arXiv preprint arXiv:2506.23392},
  year   = {2025}
}

Comments

This is the first part of a series of two papers (that were previously one single paper). The second part is "Hitchin grafting representations II: Dynamics" [2407.07748v2]. Changes in version 2: a proof was corrected. 56 pages, 4 figures, comments welcome!

R2 v1 2026-07-01T03:38:45.113Z