Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On fields of definition of arithmetic Kleinian reflection groups


Author: Mikhail Belolipetsky
Journal: Proc. Amer. Math. Soc. 137 (2009), 1035-1038
MSC (2000): Primary 30F40, 20F55, 22E40
Published electronically: September 25, 2008
MathSciNet review: 2457444
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the degrees of the real fields of definition of arithmetic Kleinian reflection groups are bounded by $ 35$.


References [Enhancements On Off] (What's this?)

  • 1. Ian Agol, Finiteness of arithmetic Kleinian reflection groups, International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 951–960. MR 2275630
  • 2. 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
  • 3. T. Chinburg, Volumes of hyperbolic manifolds, J. Differential Geom. 18 (1983), no. 4, 783–789 (1984). MR 730927
  • 4. Ted Chinburg and Eduardo Friedman, The smallest arithmetic hyperbolic three-orbifold, Invent. Math. 86 (1986), no. 3, 507–527. MR 860679, 10.1007/BF01389265
  • 5. D. D. Long, C. Maclachlan, and A. W. Reid, Arithmetic Fuchsian groups of genus zero, Pure Appl. Math. Q. 2 (2006), no. 2, 569–599. MR 2251482, 10.4310/PAMQ.2006.v2.n2.a9
  • 6. Colin Maclachlan and Alan W. Reid, The arithmetic of hyperbolic 3-manifolds, Graduate Texts in Mathematics, vol. 219, Springer-Verlag, New York, 2003. MR 1937957
  • 7. V. V. Nikulin, On ground fields of arithmetic hyperbolic reflection groups, preprint arXiv:0708.3991v1 [math.AG], 33 pages.
  • 8. V. V. Nikulin, On ground fields of arithmetic hyperbolic reflection groups. II, preprint arXiv:0710.0162v3 [math.AG], 27 pages.
  • 9. V. V. Nikulin, On ground fields of arithmetic hyperbolic reflection groups. III, preprint arXiv:0710.2340v3 [math.AG], 24 pages.
  • 10. È. B. Vinberg, Discrete groups generated by reflections in Lobačevskiĭ spaces, Mat. Sb. (N.S.) 72 (114) (1967), 471–488; correction, ibid. 73 (115) (1967), 303 (Russian). MR 0207853
  • 11. È. B. Vinberg, Reflective subgroups in Bianchi groups, Selecta Math. Soviet. 9 (1990), no. 4, 309–314. Selected translations. MR 1078259

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30F40, 20F55, 22E40

Retrieve articles in all journals with MSC (2000): 30F40, 20F55, 22E40


Additional Information

Mikhail Belolipetsky
Affiliation: Department of Mathematical Sciences, Durham University, Durham DH1 3LE, United Kingdom – and – Sobolev Institute of Mathematics, Koptyuga 4, 630090 Novosibirsk, Russia
Email: mikhail.belolipetsky@durham.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09590-7
Received by editor(s): November 6, 2007
Received by editor(s) in revised form: March 31, 2008
Published electronically: September 25, 2008
Additional Notes: The author was partially supported by EPSRC grant EP/F022662/1
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.