On normal subgroups in the fundamental groups of complex surfaces

1998/08/18 by Michael Kapovich, Kapovich, Michael · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.GT

paper · pdf · doi:10.48550/arxiv.math/9808085

arxiv created 1998/08/18 · arxiv updated 2009/11/30

Abstract

We show that for each aspherical compact complex surface X whose fundamental group π fits into a short exact sequence 1→ K → π→ π₁(S) → 1 where S is a compact hyperbolic Riemann surface and the group K is finitely-presentable, there is a complex structure on S and a nonsingular holomorphic fibration f: X→ S which induces the above short exact sequence. In particular, the fundamental groups of compact complex-hyperbolic surfaces cannot fit into the above short exact sequence. As an application we give the first example of a non-coherent uniform lattice in PU(2,1).

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