Atlas: On fundamental groups of complex hyperbolic surfaces by Michael Kapovich

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International Conference on Non-Positive Curvature in Group Theory, Topology, and Geometry
May 28-31, 1998
Vanderbilt University
Nashville, TN, USA

Organizers
B. Hughes, M. Mihalik, E. Prassidis, J. Ratcliffe, K. Ruane, M. Sapir, E. Schechter

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On fundamental groups of complex hyperbolic surfaces
by
Michael Kapovich
University of Utah

We show that the fundamental group of a compact complex-hyperbolic surface M cannot fit into a short exact sequence

1 --> \pi₁(S₁) --> \pi₁(M) --> \pi₁(S₂) --> 1

where S₁, S₂ are hyperbolic Riemann surfaces. As an application of the technique used in the proof we show that there are compact complex-hyperbolic surfaces whose fundamental groups are not coherent.

Date received: April 16, 1998