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Two-generator discrete subgroups of PSL (2, R) / [electronic resource] Jane Gilman.

By: Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 561Publication details: Providence, R.I. : American Mathematical Society, c1995.Description: 1 online resource (x, 204 p. : ill.)ISBN:
  • 9781470401405 (online)
Subject(s): Additional physical formats: Two-generator discrete subgroups of PSL (2, R) /DDC classification:
  • 510 s 515/.223 20
LOC classification:
  • QA3 .A57 no. 561 QA335
Online resources:
Contents:
I. Introduction 1. Introduction 2. The triangle algorithm and the acute triangle theorem 3. The discreteness theorem II. Preliminaries 4. Triangle groups and their tilings 5. Pentagons 6. A summary of formulas for the hyperbolic trigonometric functions and some geometric corollaries 7. The Poincar�e polygon theorem and its partial converse; Knapp's theorem and its extension III. Geometric equivalence and the discreteness theorem 8. Constructing the standard acute triangles and standard generators 9. Generators and Nielsen equivalence for the $(2,3, n)t = 3$; $k = 3$ case 10. Generators and Nielsen equivalence for the $(2,4, n)t = 2$; $k = 2$ case 11. Constructing the standard $(2,3,7)k=2;\ t=9$ pentagon: Calculating the 2-2 spectrum 12. Finding the other seven and proving geometric equivalence 13. The proof of the discreteness theorem IV. The real number algorithm and the Turing machine algorithm 14. Forms of the algorithm V. Appendix Appendix A. Verify Matelski-Beardon count Appendix B. A summary of notation
Item type: E-BOOKS
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IMSc Library Link to resource Available EBK13014

"September 1995, volume 117, number 561 (fourth of 5 numbers)."

Includes bibliographical references (p. 201-204).

I. Introduction 1. Introduction 2. The triangle algorithm and the acute triangle theorem 3. The discreteness theorem II. Preliminaries 4. Triangle groups and their tilings 5. Pentagons 6. A summary of formulas for the hyperbolic trigonometric functions and some geometric corollaries 7. The Poincar�e polygon theorem and its partial converse; Knapp's theorem and its extension III. Geometric equivalence and the discreteness theorem 8. Constructing the standard acute triangles and standard generators 9. Generators and Nielsen equivalence for the $(2,3, n)t = 3$; $k = 3$ case 10. Generators and Nielsen equivalence for the $(2,4, n)t = 2$; $k = 2$ case 11. Constructing the standard $(2,3,7)k=2;\ t=9$ pentagon: Calculating the 2-2 spectrum 12. Finding the other seven and proving geometric equivalence 13. The proof of the discreteness theorem IV. The real number algorithm and the Turing machine algorithm 14. Forms of the algorithm V. Appendix Appendix A. Verify Matelski-Beardon count Appendix B. A summary of notation

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Mode of access : World Wide Web

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The Institute of Mathematical Sciences, Chennai, India