A construction of representations of 3-manifold groups into PU(2,1) through Lefschetz fibrations

DOI10.5802/AFST.1751arXiv1909.10229MaRDI QIDQ6325792

Publication date: 23 September 2019

Abstract: We obtain infinitely many (non-conjugate) representations of 3-manifold fundamental groups into a lattice in the holomorphic isometry group of complex hyperbolic space. The lattice is an orbifold fundamental group of a branched covering of the projective plane along an arrangement of hyperplanes constructed by Hirzebruch. The 3-manifolds are related to a Lefschetz fibration of the complex hyperbolic orbifold.

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