Título:
|
On the character variety of tunnel number 1 knots
|
Autores:
|
Hilden, Hugh Michael ;
Lozano Imízcoz, María Teresa ;
Montesinos Amilibia, José María
|
Tipo de documento:
|
texto impreso
|
Editorial:
|
Oxford University Press, 2000
|
Palabras clave:
|
Estado = Publicado
,
Materia = Ciencias: Matemáticas: Topología
,
Tipo = Artículo
|
Resumen:
|
Given a hyperbolic knot K in S3, the SL2(C) characters of?1(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 ?(K), and the trace function corresponding to the meridian of K induces a map p:?(K)?C.
The pair (?(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
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.
|