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Quasi-isometries preserve the geometric decomposition of Haken manifolds. (English) Zbl 0866.20033
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.
Reviewer: B.Leeb (Bonn)

20F65 Geometric group theory
57M50 General geometric structures on low-dimensional manifolds
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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