Volumes of Hyperbolic Three-Manifolds Associated with Modular Links
Keyword(s):
Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle PSL 2 ( Z ) ∖ PSL 2 ( R ) . A finite collection of such orbits is a collection of disjoint closed curves in a 3-manifold, in other words a link. The complement of those links is always a hyperbolic 3-manifold, and hence has a well-defined volume. We present strong numerical evidence that, in the case of the set of geodesics corresponding to the ideal class group of a real quadratic field, the volume has linear asymptotics in terms of the total length of the geodesics. This is not the case for general sets of geodesics.
1992 ◽
Vol 35
(3)
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pp. 361-370
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1980 ◽
Vol 12
(2)
◽
pp. 191-196
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2005 ◽
Vol 57
(3)
◽
pp. 375-394
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1993 ◽
Vol 117
(3)
◽
pp. 613-613
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1983 ◽
Vol 26
(2)
◽
pp. 221-231
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2015 ◽
Vol 100
(1)
◽
pp. 21-32
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