Hyperbolic geometry | 3-manifolds

Meyerhoff manifold

In hyperbolic geometry, the Meyerhoff manifold is the arithmetic hyperbolic 3-manifold obtained by surgery on the figure-8 knot complement. It was introduced by Robert Meyerhoff as a possible candidate for the hyperbolic 3-manifold of smallest volume, but the Weeks manifold turned out to have slightly smaller volume. It has the second smallest volume of orientable arithmetic hyperbolic 3-manifolds, where is the zeta function of the quartic field of discriminant . Alternatively, where is the polylogarithm and is the absolute value of the complex root (with positive imaginary part) of the quartic . Ted Chinburg showed that this manifold is arithmetic. (Wikipedia).

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Related pages

Gieseking manifold | Polylogarithm | Weeks manifold | Absolute value | Arithmetic hyperbolic 3-manifold | Hyperbolic geometry | Figure-eight knot (mathematics) | Knot complement | Dedekind zeta function | Dehn surgery | Quartic function