Mathematical Surveys and Monographs
Volume: 215;
2016;
174 pp;
Hardcover
MSC: Primary 20;
Print ISBN: 978-1-4704-2901-0
Product Code: SURV/215
List Price: $110.00
AMS Member Price: $88.00
MAA Member Price: $99.00
Electronic ISBN: 978-1-4704-3599-8
Product Code: SURV/215.E
List Price: $110.00
AMS Member Price: $88.00
MAA Member Price: $99.00
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Supplemental Materials
On Groups of PL-homeomorphisms of the Real Line
Share this pageRobert Bieri; Ralph Strebel
Richard Thompson's famous group \(F\) has the striking property
that it can be realized as a dense subgroup of the group of all
orientation-preserving homeomorphisms of the unit interval, but it can
also be given by a simple 2-generator-2-relator presentation, in fact
as the fundamental group of an aspherical complex with only two cells
in each dimension.
This monograph studies a natural generalization of \(F\) that also
includes Melanie Stein's generalized \(F\)-groups. The main
aims of this monograph are the determination of isomorphisms among the
generalized \(F\)-groups and the study of their automorphism
groups.
This book is aimed at graduate students (or teachers of graduate
students) interested in a class of examples of torsion-free infinite
groups with elements and composition that are easy to describe and
work with, but have unusual properties and surprisingly small
presentations in terms of generators and defining
relations.
Readership
Graduate students and researchers interested in geometric group theory.
Table of Contents
Table of Contents
On Groups of PL-homeomorphisms of the Real Line
- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Introduction 120
- Chapter A. Construction of Finitary PL-homeomorphisms 1332
- Chapter B. Generating Sets 2342
- Chapter C. The Subgroup of Bounded Homeomorphisms 𝐵 4362
- Chapter D. Presentations 6180
- Chapter E. Isomorphisms and Automorphism Groups 89108
- Notes 137156
- Bibliography 163182
- Index of Notation 167186
- Subject Index 171190
- Back Cover Back Cover1194