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Non-simple geodesics in hyperbolic 3-manifolds

  • Kerry N. Jones (a1) and Alan W. Reid (a2)

Chinburg and Reid have recently constructed examples of hyperbolic 3-manifolds in which every closed geodesic is simple. These examples are constructed in a highly non-generic way and it is of interest to understand in the general case the geometry of and structure of the set of closed geodesics in hyperbolic 3-manifolds. For hyperbolic 3-manifolds which contain immersed totally geodesic surfaces there are always non-simple closed geodesics. Here we construct examples of manifolds with non-simple closed geodesics and no totally geodesic surfaces.

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[4] L. Clozel . On the cuspidal cohomology of arithmetic subgroups of SL(2n) and the first betti number of arithmetic 3-manifolds. Duke Math. J. 55 (1987), 475486.

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[15] M.-F. Vignéras . Arithmétique des algébres de Quaternions. Lecture Notes in Mathematics 800. (Springer-Verlag, 1980).

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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