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Inventiones mathematicae

, Volume 146, Issue 1, pp 143–192 | Cite as

Bounded geometry for Kleinian groups

  • Yair N. Minsky
Article

Abstract.

We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend only on its end invariants. Bounded geometry is a positive lower bound on the lengths of closed geodesics. When the surface is a once-punctured torus, the coefficients coincide with the continued fraction coefficients associated to the ending laminations.

Keywords

Boundary Component Homotopy Class Kleinian Group Elementary Move Pleated Surface 
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

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Yair N. Minsky
    • 1
  1. 1.SUNY at Stony Brook, Institute for Mathematical Sciences, Stony Brook, NY 11794-3651, USAUSA

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