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About: Meyerhoff manifold     Goto   Sponge   NotDistinct   Permalink

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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, Ted Chinburg showed that this manifold is arithmetic.