Resumen:
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The manifold M obtained by 0-surgery on the figure eight knot is a torus bundle over S1, and the core ? of the surgery is a section of the bundle. The pair (M,?) admits a structure as a hyperbolic cone-manifold with cone angle ??(0,2?). For ? of the form 2?/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.
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