Kapovich, Michael; Leeb, Bernhard Quasi-isometries preserve the geometric decomposition of Haken manifolds. (English) Zbl 0866.20033 Invent. Math. 128, No. 2, 393-416 (1997). 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) Cited in 1 ReviewCited in 28 Documents MSC: 20F65 Geometric group theory 57M50 General geometric structures on low-dimensional manifolds 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions Keywords:quasi-isometry invariance; fundamental groups; Haken 3-manifolds; Haken manifold groups; Haken orbifold groups; universal covers PDFBibTeX XMLCite \textit{M. Kapovich} and \textit{B. Leeb}, Invent. Math. 128, No. 2, 393--416 (1997; Zbl 0866.20033) Full Text: DOI