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

Author
Gilman, Jane, 1945- [Browse]
Format
Book
Language
English
Published/​Created
Providence, R.I. : American Mathematical Society, ©1995.
Description
x, 204 pages : illustrations ; 26 cm.

Availability

Copies in the Library

Location Call Number Status Location Service Notes
Lewis Library - Stacks QA3 .A57 no.561 Browse related items Request

    Details

    Subject(s)
    Series
    Summary note
    Let [italic capital]A and [italic capital]B be elements of [italic capitals]PSL (2, [bold]R) and let [italic capital]G be the group they generate. Assume that [italic capital]G is non-elementary. The discreteness problem is the problem of finding an algorithm to determine whether [italic capital]G is or is not discrete. In this monograph we provide what one hopes is the definitive solution to the discreteness problem. We present the first complete geometric solution to the discreteness problem building upon the cases done by Gilman and Maskit. We explain why the discreteness problem requires an algorithmic solution, and translate the geometric algorithm into a purely computational algorithm, one which allows all standard computations with real numbers.
    Notes
    "September 1995, volume 117, number 561 (fourth of 5 numbers)."
    Bibliographic references
    Includes bibliographical references.
    Contents
    • Part I. Introduction ; t Introduction
    • The triangle algorithm and the acute triangle theorem
    • The discreteness theorem
    • Part II. Preliminaries ; Triangle groups and their tilings
    • Pentagons
    • A summary of formulas for the hyperbolic trigonometric functions and some geometric corollaries
    • The Poincaré polygon theorem and its partial converse; Knapp's theorem and its extension
    • Part III. Geometric equivalence and the discreteness theorem ; Constructing the standard acute triangles and standard generators
    • Generators and Nielsen equivalence for the (2, 3, [italic]n)[italic]t = 3; [italic]k = 3 case
    • Generators and Nielsen equivalence for the (2, 4, [italic]n)[italic]t = 2; [italic]k = 2 case
    • Constructing the standard (2, 3, 7)[italic]k = 2; [italic]t = 9 pentagon : calculating the 2-2 spectrum
    • Finding the other seven and proving geometric equivalence
    • The proof of the discreteness theorem
    • Part IV. The real number algorithm and the Turing machine algorithm ; Forms of the algorithm
    • Part V. Appendix ; Appendix A. Verify Matelski-Beardon count
    • Appendix B. A summary of notation.
    Other title(s)
    Two-generator discrete subgroups of [italic capitals]PSL (2, [bold]R)
    ISBN
    • 0821803611 ((acid-free))
    • 9780821803615 ((acid-free))
    LCCN
    95009531
    OCLC
    32626357
    Statement on language in description
    Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage. Read more...
    Other views
    Staff view

    Supplementary Information