Kähler manifolds and fundamental groups of negatively $δ$-pinched manifolds

Details Kähler manifolds and fundamental groups of negatively $δ$-pinched manifolds Kähler manifolds and fundamental groups of negatively $δ$-pinched manifolds

2003-12-07

arxiv.org/abs/math/0312143v1

Mathematics

Differential Geometry

Version with additional supplementary material to appear in Intern.J.Math

Scientific paper

The fundamental group of a Riemannian manifold with $\delta$-pinched negative curvature, $\delta >1/4$, cannot be the fundamental group of a quasicompact K\"ahler manifold. The proof also implies that a non-uniform lattice in $F_{4(-20)}$ cannot be the fundamental group of a quasicompact K\"ahler manifold. We also construct examples in the spirit of Gromov-Thurston to show that our result is a non-trivial extension of the previously known result that a non-uniform lattice in real hyperbolic space in dimension at least 3 cannot be the fundamental group of a quasicompact K\"ahler manifold.

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