Jørgensen's inequality for classical Schottky groups of real type

Hiroki SATO

doi:10.2969/jmsj/05040945

Hiroki SATO

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JOURNAL FREE ACCESS

1998 Volume 50 Issue 4 Pages 945-968

DOI https://doi.org/10.2969/jmsj/05040945

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Published: 1998 Received: July 27, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Mitsuru Nakai on his sixtieth birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: ABSTRACT Details: Wrong : In this paper we consider Jørgensen's inequalities for classical Schottky groups of the real type. The infimum of Jørgensen's numbers for groups of types II, V and VII are 16, 4(1+√<2>)² and 4(1+√<2>)², respectively, each of which is the best possible for Jørgensen's inequality.
Right : In this paper we consider Jørgensen's inequalities for classical Schottky groups of the real type. The infimum of Jørgensen's numbers for groups of types II, V and VII are 16, 4(1+√2)² and 4(1+√2)², respectively, each of which is the best possible for Jørgensen's inequality.

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Gilman, A geometric approach to Jørgensen's inequality, Adv. in Math. 85 (1991), 193-197.
2) T. Jørgensen, On discrete groups of Möbius transformations, Amer. J. Math. 98 (1976), 739-749.
3) T. Jørgensen, A. Lascurain and T. Pignataro, Translation extensions of the classical modular groups, Complex Variables 19 (1992), 205-209.
4) B. M. Neumann, Die Automorphismengruppe der freien Gruppen, Math. Ann. 107 (1932), 367-386.
5) H. Sato, Classical Schottky groups of real type of genus two, I, Tohoku Math. J. 40 (1988), 51-75.
6) H. Sato, Classical Schottky groups of real type of genus two, II, Tohoku Math. J. 43 (1991), 449-472.
7) H. Sato, Jørgensen's inequality for purely hyperbolic groups, Rep. Fac. Sci. Shizuoka Univ. 26 (1992), 1-9.
8) H. Sato and R. Yamada, Some extreme Kleinian groups for Jørgensen's inequalities, Rep. Fac. Sci. Shizuoka Univ. 27 (1993), 1-8.
9) H. Sato, Jørgensen's inequality for classical Schottky groups of real type, RIMS Koukyuroku 882, Kyoto Univ. (1994), 89-103.
10) H. Sato, Classical Schottky groups of real type of genus two, III, Tohoku Math. J. 49 (1997), 485- 502.
11) H. Sato, Jørgensen's inequality for classical Schottky groups of real type, II, in preparation.

Right : [1] J. Gilman, A geometric approach to Jørgensen's inequality, Adv. in Math. 85 (1991), 193-197.
[2] T. Jørgensen, On discrete groups of Möbius transformations, Amer. J. Math. 98 (1976), 739-749.
[3] T. Jørgensen, A. Lascurain and T. Pignataro, Translation extensions of the classical modular groups, Complex Variables 19 (1992), 205-209.
[4] B. M. Neumann, Die Automorphismengruppe der freien Gruppen, Math. Ann. 107 (1932), 367-386.
[5] H. Sato, Classical Schottky groups of real type of genus two, I, Tôhoku Math. J. 40 (1988), 51-75.
[6] H. Sato, Classical Schottky groups of real type of genus two, II, Tôhoku Math. J. 43 (1991), 449-472.
[7] H. Sato, Jørgensen's inequality for purely hyperbolic groups, Rep. Fac. Sci. Shizuoka Univ. 26 (1992), 1-9.
[8] H. Sato and R. Yamada, Some extreme Kleinian groups for Jørgensen's inequalities, Rep. Fac. Sci. Shizuoka Univ. 27 (1993), 1-8.
[9] H. Sato, Jørgensen's inequality for classical Schottky groups of real type, RIMS Koukyuroku 882, Kyoto Univ. (1994), 89-103.
[10] H. Sato, Classical Schottky groups of real type of genus two, III, Tôhoku Math. J. 49 (1997), 485-502.
[11] H. Sato, Jørgensen's inequality for classical Schottky groups of real type, II, in preparation.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

Abstract

In this paper we consider Jørgensen's inequalities for classical Schottky groups of the real type. The infimum of Jørgensen's numbers for groups of types II, V and VII are 16, 4(1+√2)² and 4(1+√2)², respectively, each of which is the best possible for Jørgensen's inequality.

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