Fundamental groups of finite volume, bounded negatively curved 4-manifolds are not 3-manifold groups

Grigori Avramidi, T. Tam Nguyen Phan, Yunhui Wu

We study noncompact, complete, finite volume, Riemannian 4-manifolds $M$ with sectional curvature $-1<K<0$. We prove that ${\pi }_{1}M$ cannot be a 3-manifold group. A classical theorem…