Complex Projective Spaces Via Surface Groups Representations

Arnaud Maret

My plan is to explain how complex projective spaces can be identified with components of totally elliptic representations of the fundamental group of a punctured sphere into PLS(2,R). I will explain how this identification realizes the pure mapping class group of the punctured sphere as a subgroup of the group of Hamiltonian diffeomorphisms of the complex projective space.

https://www.ias.edu/video/complex-projective-spaces-surface-groups-representations