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The arithmeticity of certain torus bundle cone 3-manifolds and hyperbolic surface bundle 3-manifolds; and an enhanced arithmeticity test

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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (1997) The arithmeticity of certain torus bundle cone 3-manifolds and hyperbolic surface bundle 3-manifolds; and an enhanced arithmeticity test. In KNOTS '96. World Scientific Publishing Co, River Edge, pp. 73-80. ISBN 981-02-3093-1



Abstract

The manifold M obtained by 0-surgery on the figure eight knot is a torus bundle over S1, and the core Σ of the surgery is a section of the bundle. The pair (M,Σ) admits a structure as a hyperbolic cone-manifold with cone angle α∈(0,2π). For α of the form 2π/n with n>1, it is a hyperbolic orbifold (M,n). Using an arithmeticity test from one of their previous papers, the authors prove that (M,n) is arithmetic if and only if n=2,3. The test has been enhanced by eliminating an unnecessary condition. Taking branched coverings of the (M,n) yields an explicit construction of many hyperbolic surface bundles over S1, both arithmetic and non-arithmetic.


Item Type:Book Section
Additional Information:

Proceedings of the International Conference and Workshop on Knot Theory held at Waseda University, Tokyo, July 22–26, 1996

Uncontrolled Keywords:hyperbolic 3-manifold
Subjects:Sciences > Mathematics > Topology
ID Code:22216
Deposited On:05 Jul 2013 15:27
Last Modified:12 Dec 2018 15:13

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