# Shearing deformations of Hitchin representations and the Atiyah-Bott-Goldman symplectic form

## TL;DR

This paper investigates shearing deformations within Hitchin components of surface group representations and computes their pairing with the Atiyah-Bott-Goldman symplectic form, revealing geometric and dynamical insights.

## Contribution

It introduces and analyzes shearing deformations in Hitchin components and calculates their symplectic pairing, advancing understanding of the geometric structure of character varieties.

## Key findings

- Explicit computation of the pairing for shearing deformations
- Enhanced understanding of the symplectic geometry of Hitchin components
- Connections between deformations and dynamical properties of representations

## Abstract

The Hitchin component Hit_n(S) of a closed surface S is a preferred component of the character variety X_PSL_n(R)(S) consisting of homomorphisms from the fundamental group pi_1(S) to the Lie group PSL_n(R)(S), whose elements enjoy remarkable geometric and dynamical properties. We consider a certain type of deformations of the elements of Hit_n(S), called shearing deformations, and compute their pairing for the Atiyah-Bott-Goldman symplectic form of the character variety.