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Degeneration of hyperbolic structures on the figure-eight knot complement and points of finite order on an elliptic curve

Degeneration of hyperbolic structures on the figure-eight knot complement and points of finite order on an elliptic curve

In this paper, we consider a hyperbolic structure on a manifold to be a Riemannian metric of constant sectional curvature −1 which is not necessarily complete. A hyperbolic 3-manifold is an orientable 3-manifold with a hyperbolic structure. It is well known that the complement of the figure-eight knot K in …