2026-06-27T10:49:35Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/586462023-08-28T05:40:34Zcom_20.500.14352_14col_20.500.14352_15

Hilden, Hugh Michael Lozano Imízcoz, María Teresa Montesinos Amilibia, José María 2023-06-20T18:47:53Z 2023-06-20T18:47:53Z 2000 0024-6107 10.1112/S0024610700001605 https://hdl.handle.net/20.500.14352/58646 http://jlms.oxfordjournals.org/content/62/3/938 http://www.cambridge.org/ Given a hyperbolic knot K in S3, the SL2(C) characters ofπ1(S3−K) form an algebraic variety Cˆ(K). The algebraic component containing the character of the complete hyperbolic structure of S3−K is an algebraic curve CˆE(K). The desingularization of the projective curve corresponding to CˆE(K) is a Riemann surface Σ(K), and the trace function corresponding to the meridian of K induces a map p:Σ(K)→C. The pair (Σ(K),p) contains a great deal of information about the knot K and its hyperbolic structure. It can be described by a polynomial rE[K](y,z). There is an algebraic number yh which is a particular critical point of p in the interval (−2,2). It defines an angle 0<αh<2π with yh=2cos(αh/2), called the limit of hyperbolicity. The minimal polynomial hK(y) of yh is called the h-polynomial of K. The calculation of these invariants is in general quite complicated. In this paper the authors develop a method to calculate rE[K](y,z) and hK(y) for any tunnel number one knot, and they apply the method to the knots 10139 and 10161. metadata only access On the character variety of tunnel number 1 knots journal article