Year: 2019
Type: preprint
Abstract: The Hitchin component is a connected component of the character variety of reductive group homomorphisms from the fundamental group of a closed surface S of genus greater than 1 to the Lie group PSL_m(R). The Teichmuller space of S naturally embeds into the Hitchin component. The limit points in the Thurston compactification of the Teichmuller space are well-understood. Our main goal is to provide non-trivial sufficient conditions on a sequence of Hitchin representations so that the limit of this sequence in the Parreau boundary can be described as an action on a tree. These non-trivial conditions are given in terms of Fock-Goncharov coordinates on moduli spaces of generic tuples of flags.
Source: arXiv (Cornell University)
Author: Martone, Giuseppe
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394664909