, Volume 128, Issue 2, pp 393-416

Quasi-isometries preserve the geometric decomposition of Haken manifolds

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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.

Oblatum 27-III-1996 & 5-IX-1996