Geometric & Functional Analysis GAFA

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

Divergence in 3-manifold groups

  • S. M. Gersten


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.


Fundamental Group Universal Cover Quadratic Divergence Hyperbolic Geometry Nonpositive Curvature 
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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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