Pinching surface groups in complex hyperbolic plane (Q1397896)

The paper contains the proof of the following theorem: Let \(M\) be a closed orientable surface of genus \(g\geq 2\) and \(\gamma\in\pi = \pi _1(M)\) be a non-trivial element represented by a simple closed loop separating \(M\). Then there exists a discrete faithful representation \(\rho :\pi\to\;\)PU(2,1) such that: (1) \(\rho (\pi )\) is geometrically finite, (2) any maximal parabolic group of \(\rho (\pi )\) is generated by a conjugate of \(\rho (\gamma )\), (3) the quotient \(H^2_{\mathbb C}/\rho (\pi )\) is diffeomorphic to \(TM\), and (4) the Toledo invariant \(\tau (\rho )\) vanishes.