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A construction of representations of 3-manifold groups into PU(2,1) through Lefschetz fibrations (1909.10229v1)
Published 23 Sep 2019 in math.GT
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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