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Geometric & Functional Analysis GAFA

, Volume 4, Issue 6, pp 633–647 | Cite as

Divergence in 3-manifold groups

  • S. M. Gersten
Article

Abstract

The divergence of the fundamental group of compact irreducible 3-manifolds satisfying Thurston's geometrization conjecture is calculated. For every closed Haken 3-manifold group, the divergence is either linear, quadratic or exponential, where quadratic divergence occurs precisely for graph manifolds and exponential divergence occurs when a geometric piece has hyperbolic geometry. An example is given of a closed 3-manifoldN with a Riemannian metric of nonpositive curvature such that the divergence is quadratic and such that there are two geodesic rays in the universal cover∼N whose divergence is precisely quadratic, settling in the negative a question of Gromov's.

Keywords

Fundamental Group Universal Cover Quadratic Divergence Hyperbolic Geometry Nonpositive Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • S. M. Gersten
    • 1
  1. 1.Mathematics DepartmentUniversity of UtahSalt Lake CityUSA

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