The Poincaré holonomy variety (or $sl(2, C)$-oper) is the set of holonomy representations of all complex projective structures on a Riemann surface. It is a complex analytic subvariety of the $PSL(2, C)$ character variety of the underlying topological surface. In this talk, we consider the intersection of such subvarieties for different Riemann surface structures, and we prove the discreteness of such an intersection. As a corollary, we reprove Bers’ simultaneous uniformization theorem, without any quasiconformal deformation theory.

- All seminars.
- Seminars for 2022

Last updated: 20 Apr 2024