Kähler manifolds and fundamental groups of negatively δ-pinched manifolds
Jürgen Jost and Yi-Hu Yang
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Submission date: 08. Dec. 2003
published in: International journal of mathematics, 15 (2004) 2, p. 151-167
DOI number (of the published article): 10.1142/S0129167X04002247
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In this note, we will show that the fundamental group of any negatively -pinched () manifold can't be the fundamental group of a quasi-compact Kähler manifold. As a consequence of our proof, we also show that any nonuniform lattice in cannot be the fundamental group of a quasi-compact Kähler manifold. The corresponding result for uniform lattices was proved by Carlson and Hernández. Finally, we follow Gromov and Thurston to give some examples of negatively -pinched manifolds () of finite volume which, as topological manifolds, admit no hyperbolic metric with finite volume under any smooth structure. This shows that our result for -pinched manifolds is a nontrivial generalization of the fact that no nonuniform lattice in is the fundamental group of a quasi-compact Kähler manifold.