

Preprint 103/2003
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
Pages: 16
published in: International journal of mathematics, 15 (2004) 2, p. 151-167
DOI number (of the published article): 10.1142/S0129167X04002247
Bibtex
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Abstract:
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.