A small arithmetic hyperbolic three-manifold

Author:
Ted Chinburg

Journal:
Proc. Amer. Math. Soc. **100** (1987), 140-144

MSC:
Primary 57S30; Secondary 22E40, 30F40, 51M10, 57N10

DOI:
https://doi.org/10.1090/S0002-9939-1987-0883417-4

MathSciNet review:
883417

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Abstract | References | Similar Articles | Additional Information

Abstract: The hyperbolic three-manifold which results from Dehn surgery on the complement of a figure-eight knot in is arithmetic.

**[1]**A. Borel,*Commensurability classes and volumes of hyperbolic**-manifolds*, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)**8**(1981), 1-33. MR**616899 (82j:22008)****[2]**T. Chinburg and E. Friedman,*The smallest arithmetic hyperbolic three-orbifold*, Invent. Math. (to appear). MR**860679 (88a:22022)****[3]**H. J. Godwin,*On quartic fields of signature one with small discriminant*, Quart. J. Math. Oxford**8**(1957), 214-222. MR**0097375 (20:3844)****[4]**R. Meyerhoff,*A lower bound for the volume of hyperbolic**-manifolds*, preprint (1982).**[5]**J. Milnor,*Hyperbolic geometry: The first 150 years*, Bull. Amer. Math. Soc. (N.S.)**6**(1982) 9-24. MR**634431 (82m:57005)****[6]**R. Riley,*A quadratic parabolic group*, Math. Proc. Cambridge Philos. Soc.**77**(1975), 281-288. MR**0412416 (54:542)****[7]**W. Thurston,*The geometry and topology of**-manifolds*, Princeton Univ. preprint (1978).**[8]**-,*Three dimensional manifolds, Kleinian groups and hyperbolic geometry*, Bull. Amer. Math. Soc. (N.S.)**6**(1982), 357-381. MR**648524 (83h:57019)****[9]**J. Weeks,*Hyperbolic structures on three-manifolds*, Princeton Ph.D. thesis (1985).

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0883417-4

Article copyright:
© Copyright 1987
American Mathematical Society