Quasi-isometries preserve the geometric decomposition of Haken manifolds
- Cite this article as:
- Kapovich, M. & Leeb, B. Invent math (1997) 128: 393. doi:10.1007/s002220050145
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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.