Automorphisms of character varieties
Julien March\'e, Christopher-Lloyd Simon

TL;DR
This paper investigates the automorphism group of the SL(2,C) character variety of closed surfaces, revealing it as a finite extension of the mapping class group, and characterizes valuations from measured laminations.
Contribution
It establishes a precise relationship between automorphisms of character varieties and the mapping class group, and characterizes valuations from measured laminations.
Findings
Automorphism group is a finite extension of the mapping class group.
Provides a simple characterization of valuations from measured laminations.
Enhances understanding of the structure of character varieties.
Abstract
We show that the algebraic automorphism group of the SL(2,C) character variety of a closed orientable surface with negative Euler characteristic is a finite extension of its mapping class group. Along the way, we provide a simple characterization of the valuations on the character algebra coming from measured laminations.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Algebraic Geometry and Number Theory
