Signature, Toledo invariant, and the surface group representations in Hermitian semisimple Lie groups

People study higher Teichmuller theory and using several invariants, one tries to characterize the representations. We give a unifying formula between (Atiyah-Patodi-Singer) signature, Toledo invariant and rho invariant for the surface group (with boundary) representations into Hermitian semisimple Lie groups. This is a joint work with P. Pansu and X. Wan.