Quasi-isometries preserve the geometric decomposition of Haken manifolds
We prove quasi-isometry invariance of the canonical decomposition for fundamental groups of Haken 3-manifolds with zero Euler characteristic. We show that groups quasi-isometric to Haken manifold groups with nontrivial canonical decomposition are finite extensions of Haken orbifold groups. As a by-product we describe all 2-dimensional quasi-flats in the universal covers of non-geometric Haken manifolds.
KeywordsManifold Fundamental Group Universal Cover Euler Characteristic Finite Extension
Unable to display preview. Download preview PDF.