Hyperbolic invariants of knots and links

Authors:
Colin Adams, Martin Hildebrand and Jeffrey Weeks

Journal:
Trans. Amer. Math. Soc. **326** (1991), 1-56

MSC:
Primary 57M25; Secondary 22E40, 30F40, 57N10

DOI:
https://doi.org/10.1090/S0002-9947-1991-0994161-2

MathSciNet review:
994161

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Tables of values for the hyperbolic volume, number of symmetries, cusp volume and conformal invariants of the cusps are given for hyperbolic knots through ten crossings and hyperbolic links of and components through crossings. The horoball patterns and the canonical triangulations are displayed for knots through eight crossings and for particularly interesting additional examples of knots and links.

**[1]**C. Adams,*Thrice-punctured spheres in hyperbolic*-*manifolds*, Trans. Amer. Math. Soc.**287**(1985), 645-656. MR**768730 (86k:57008)****[2]**-,*The noncompact hyperbolic*-*manifold of minimal volume*, Proc. Amer. Math. Soc.**100**(1987), 601-606. MR**894423 (88m:57018)****[3]**-,*Volumes of*-*cusped hyperbolic*-*manifolds*, J. London Math. Soc. (2)**38**(1988), 555-565. MR**972138 (89k:22020)****[4]**K. Boroczky,*Packing of spheres in spaces of constant curvature*, Acta Math. Acad. Sci. Hungar.**32**(1978), 243-326. MR**512399 (80h:52014)****[5]**G. Burde and H. Zieschang,*Knots*, De Gruyter Studies in Mathematics, vol. 5, De Gruyter, Berlin, 1985. MR**808776 (87b:57004)****[6]**L. R. Ford,*Automorphic functions*, McGraw-Hill, New York, 1929.**[7]**R. Meyerhoff,*Sphere packing and volume in hyperbolic*-*space*, Comment. Math. Helv.**61**(1986), 271-278. MR**856090 (88e:52023)****[8]**R. Meyerhoff and D. Ruberman,*The Chern-Simons invariant and mutation*, J. Differential Geom. (to appear). MR**1030667 (91j:57017)****[9]**J. Milnor,*Hyperbolic geometry*:*the first**years*, Bull. Amer. Math. Soc.**6**(1982), 9-23. MR**634431 (82m:57005)****[10]**R. Riley,*An elliptical path from parabolic representations to hyperbolic structures*, Lecture Notes in Math., vol. 722, Springer-Verlag, 1979, pp. 99-133. MR**547459 (81e:57011)****[11]**D. Rolfsen,*Knots and links*, Publish or Perish, Berkeley, Calif., 1976. MR**0515288 (58:24236)****[12]**D. Ruberman,*Mutations and volumes of knots in*, Invent. Math.**90**(1987), 189-215. MR**906585 (89d:57018)****[13]**W. Thurston,*The geometry and topology of*-*manifolds*, Lecture notes, Princeton University, 1978-79.**[14]**W. Thurston,*Three-dimensional manifolds, Kleinian groups and hyperbolic geometry*, Bull. Amer. Math. Soc.**6**(1982), 357-381. MR**648524 (83h:57019)****[15]**J. Weeks,*Hyperbolic structures on*-*manifolds*, Ph. D. dissertation, Princeton University, 1985.**[16]**N. Wielenberg,*Hyperbolic*-*manifolds which share a fundamental polyhedron*, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, Princeton Univ. Press, Princeton, N.J., 1981, pp. 505-513. MR**624835 (82i:57012)**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
57M25,
22E40,
30F40,
57N10

Retrieve articles in all journals with MSC: 57M25, 22E40, 30F40, 57N10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1991-0994161-2

Keywords:
Hyperbolic -manifold,
hyperbolic volume,
cusp volume,
horoball pattern

Article copyright:
© Copyright 1991
American Mathematical Society