A small arithmetic hyperbolic three-manifold

A small arithmetic hyperbolic three-manifold
HTML articles powered by AMS MathViewer

by Ted Chinburg PDF

Proc. Amer. Math. Soc. 100 (1987), 140-144 Request permission

The hyperbolic three-manifold which results from $(5,1)$ Dehn surgery on the complement of a figure-eight knot in ${S^3}$ is arithmetic.

References

A. Borel, Commensurability classes and volumes of hyperbolic $3$-manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 8 (1981), no. 1, 1–33. MR 616899
Ted Chinburg and Eduardo Friedman, The smallest arithmetic hyperbolic three-orbifold, Invent. Math. 86 (1986), no. 3, 507–527. MR 860679, DOI 10.1007/BF01389265
H. J. Godwin, On quartic fields of signature one with small discriminant, Quart. J. Math. Oxford Ser. (2) 8 (1957), 214–222. MR 97375, DOI 10.1093/qmath/8.1.214

A lower bound for the volume of hyperbolic

-manifolds

John Milnor, Hyperbolic geometry: the first 150 years, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 1, 9–24. MR 634431, DOI 10.1090/S0273-0979-1982-14958-8
Robert Riley, A quadratic parabolic group, Math. Proc. Cambridge Philos. Soc. 77 (1975), 281–288. MR 412416, DOI 10.1017/S0305004100051094

The geometry and topology of

-manifolds

William P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357–381. MR 648524, DOI 10.1090/S0273-0979-1982-15003-0

Hyperbolic structures on three-manifolds