Computation of Hyperbolic Structures in Knot Theory

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Weeks, Jeffrey R.;
  • Subject: 57M25, 57M50 | Mathematics - Geometric Topology
    arxiv: Mathematics::Geometric Topology

This chapter from the upcoming Handbook of Knot Theory (eds. Menasco and Thistlethwaite) shows how to construct hyperbolic structures on link complements and perform hyperbolic Dehn filling. Along with a new elementary exposition of the standard ideas from Thurston's wo... View more
  • References (8)

    [1] C. Adams, “Hyperbolic knots”, this volume.

    [2] C. Gordon, “Dehn surgery”, this volume.

    [4] J. Weeks, “Convex hulls and isometries of cusped hyperbolic 3- manifolds”, Topology Appl. 52 (1993) 127-149.

    [5] S. Henry and J. Weeks, “Symmetry groups of hyperbolic knots and links”, J. Knot Theory and Its Ramifications 1 (1992) 185-201.

    [6] C. Hodgson and J. Weeks, “Symmetries, isometries and length spectra of closed hyperbolic 3-manifolds”, Exp. Math. 3 (1994) 261-274.

    [7] C. Adams, M. Hildebrand and J. Weeks, “Hyperbolic invariants of knots and links”, Trans. Amer. Math. Soc. 326 (1991) 1-56.

    [9] W.P. Thurston, “Three dimensional manifolds, Kleinian groups and hyperbolic geometry”, Bull. (New Series) Amer. Math. Soc. 6 (1982) 357-381.

    [10] W.P. Thurston, Three-dimensional geometry and topology (1997) Princeton Mathematical series 35, Ed. S. Levy, (Princeton University Press, Princeton, USA).

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