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Hugh M. Hilden María Teresa Lozano Jos María Montesinos-Amilibia 《Topology and its Applications》2005,150(1-3):267-288
If K is a hyperbolic knot in S3, an algebraic component of its character variety containing one holonomy of the complete hyperbolic structure of finite volume of S3K is an algebraic curve . The traces of the peripheral elements of K define polynomial functions in , which are related in pairs by polynomials (peripheral polynomials). These are determined by just two adjacent peripheral polynomials. The curves defined by the peripheral polynomials are all birationally equivalent to , with only one possible exception. The canonical peripheral polynomial relating the trace of the meridian with the trace of the canonical longitude of K, is a factor of the A-polynomial. 相似文献
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R.?Antonio Gon?alves J.?A.?Martínez Alfaro? A.?Montesinos-Amilibia? M.?C.?Romero-Fuster? 《Bulletin of the Brazilian Mathematical Society》2007,38(2):157-178
We define the relative mean curvature directions on surfaces immersed in ℝn, n ≥ 4, generalizing the concept of mean curvature directions for surfaces in 4-space studied by Mello. We obtain their differential
equations and study their corresponding generic configurations.
*Work partially supported by DGCYT grant no. MTM2004-03244 and Unimontes-BR.
†Work partially supported by DGCYT grant no. MTM2004-03244.
‡Work partially supported by DGCYT grant no. BFM2003-0203. 相似文献
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Hilden Hugh M.; Lozano Maria Teresa; Montesinos-Amilibia Jose Maria 《Journal London Mathematical Society》2000,62(3):938-950
For a hyperbolic knot, the excellent component of the charactercurve is the one containing the complete hyperbolic structureon the complement of the knot. The paper explains a method ofcomputing the excellent component of the character variety oftunnel number 1 knots. 相似文献
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Hilden Hugh M.; Lozano Maria Teresa; Montesinos-Amilibia Jose Maria 《Bulletin London Mathematical Society》1999,31(3):354-366
One important invariant of a closed Riemannian 3-manifold isthe ChernSimons invariant [1]. The concept was generalizedto hyperbolic 3-manifolds with cusps in [11], and to geometric(spherical, euclidean or hyperbolic) 3-orbifolds, as particularcases of geometric cone-manifolds, in [7]. In this paper, westudy the behaviour of this generalized invariant under changeof orientation, and we give a method to compute it for hyperbolic3-manifolds using virtually regular coverings [10]. We confineourselves to virtually regular coverings because a coveringof a geometric orbifold is a geometric manifold if and onlyif the covering is a virtually regular covering of the underlyingspace of the orbifold, branched over the singular locus. Thereforeour work is the most general for the applications in mind; namely,computing volumes and ChernSimons invariants of hyperbolicmanifolds, using the computations for cone-manifolds for whicha convenient Schläfli formula holds (see [7]). Among otherresults, we prove that every hyperbolic manifold obtained asa virtually regular covering of a figure-eight knot hyperbolicorbifold has rational ChernSimons invariant. We giveexplicit examples with computations of volumes and ChernSimonsinvariants for some hyperbolic 3-manifolds, to show the efficiencyof our method. We also give examples of different hyperbolicmanifolds with the same volume, whose ChernSimons invariants(mod ) differ by a rational number, as well as pairs of differenthyperbolic manifolds with the same volume and the same ChernSimonsinvariant (mod ). (Examples of this type were also obtainedin [12] and [9], but using mutation and surgery techniques,respectively, instead of coverings as we do here.) 1991 MathematicsSubject Classification 57M50, 51M10, 51M25. 相似文献
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