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 .
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!