Filtered Ends, Proper Holomorphic Mappings of Kähler Manifolds to Riemann Surfaces, and Kähler Groups |
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Authors: | Terrence Napier Mohan Ramachandran |
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Institution: | (1) Department of Mathematics, Lehigh University, Bethlehem, PA 18015, USA;(2) Department of Mathematics, SUNY at Buffalo, Buffalo, NY 14260, USA |
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Abstract: | The main result of this paper is that a connected bounded geometry complete K?hler manifold which has at least 3 filtered
ends admits a proper holomorphic mapping onto a Riemann surface. As an application, it is also proved that any properly ascending
HNN extension with finitely generated base group, as well as Thompson’s groups V, T, and F, are not K?hler. The results and techniques also yield a different proof of the theorem of Gromov and Schoen that, for a
connected compact K?hler manifold whose fundamental group admits a proper amalgamated product decomposition, some finite unramified
cover admits a surjective holomorphic mapping onto a curve of genus at least 2.
Received: January 2006, Revision: November 2006, Accepted: March 2007 |
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Keywords: | Fundamental groups potential theory |
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