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Hyperbolic structures on knot complements. (English) Zbl 0935.57017

The authors survey some of the applications of hyperbolic geometry in 3-manifold topology. In particular, the focus is to study the existence of a hyperbolic structure on knot complements in the standard 3-sphere. Some results on the volume computation of hyperbolic 3-manifolds are presented. Finally, a discussion on invariants associated with the hyperbolic structure completes the paper.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M50 General geometric structures on low-dimensional manifolds
57N10 Topology of general \(3\)-manifolds (MSC2010)

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References:

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