Hitchin grafting representations I: Geometry

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 ${\mathrm{PSL}}_d(\mathbb{R})/\mathrm{PSO}(d)$.

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!