Goldman Symplectic Form on the $\operatorname {PGL}(V)$-Hitchin Component

Zhe Sun, University of Science and Technology of China, Hefei, People's Republic of China.Tengren Zhang, National University of Singapore, Singapore.

• 1. Introduction2. Features of Hitchin representations and the Hitchin component3. Topological constructions4. Tangent cocycles for the Hitchin component5. The $(\mathcal {T},\mathcal {J})$-trivialization of $T\operatorname {Hit}_V(S)$6. The $(\mathcal {T},\mathcal {J})$-trivialization of $\operatorname {Hit}_V(S)$ is symplectic7. A symplectic basis of vector fields on $\operatorname {Hit}_V(S)$