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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
Available Online
Online Content
Ebook Central Perpetual, DDA and Subscription Titles
Memoirs of the American Mathematical Society. Backfiles 1950-2012
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Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA3 .A57 no.561
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Details
Subject(s)
Fuchsian groups
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Kleinian groups
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Teichmüller spaces
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Series
Memoirs of the American Mathematical Society ; no. 561.
[More in this series]
Memoirs of the American Mathematical Society, 0065-9266 ; no. 561
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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.
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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
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Two-generator discrete subgroups of PSL (2, R) / Jane Gilman.
id
99111704623506421
Two-generator discrete subgroups of PSL (2, R) / Jane Gilman.
id
99125251165606421