Abstract
We apply the concept of asymptotic cone to distinguish quasi-isometry classes of fundamental groups of 3-manifolds. We prove that the existence of a Seifert component in a Haken manifold is a quasi-isometry invariant of its fundamental group.
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This research was partially supported by the grant SFB 256 “Nichtlineare partielle Differentialgleichungen” and the NSF grant DMS-9306140 (Kapovich).
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Kapovich, M., Leeb, B. On asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds. Geometric and Functional Analysis 5, 582–603 (1995). https://doi.org/10.1007/BF01895833
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DOI: https://doi.org/10.1007/BF01895833