Hyperbolic 3-Manifolds With Nonintersecting Closed Geodesics |
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Authors: | Ara Basmajian Scott A Wolpert |
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Institution: | (1) Mathematics Department, University of Oklahoma, Norman, OK, 73019, U.S.A.;(2) Mathematics Department, University of Maryland, College Park, MD, 20742, U.S.A. |
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Abstract: | A hyperbolic 3-manifold is said to have the spd-property if all its closed geodesics are simple and pairwise disjoint. For a 3-manifold which supports a geometrically finite hyperbolic structure we show the following dichotomy: either the generic hyperbolic structure has the spd-property or no hyperbolic structure has the spd-property. Both cases are shown to occur. In particular, we prove that the generic hyperbolic structure on the interior of a handlebody (or a surface cross an interval) of negative Euler characteristic has the spd-property. Simplicity and disjointness are consequences of a variational result for hyperbolic surfaces. Namely, the intersection angle between closed geodesics varies nontrivially under deformation of a hyperbolic surface. |
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Keywords: | hyperbolic manifold Kleinian group |
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