On Groups of PL-homeomorphisms of the Real Line
About this Title
Robert Bieri, Johann Wolfgang Goethe-Universität Frankfurt, Frankurt am Main, Germany and Ralph Strebel, Université de Fribourg, Fribourg, Switzerland
Publication: Mathematical Surveys and Monographs
Publication Year: 2016; Volume 215
ISBNs: 978-1-4704-2901-0 (print); 978-1-4704-3599-8 (online)
MathSciNet review: MR3560537
MSC: Primary 20F38; Secondary 20E32, 20F05, 20F28
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.
Graduate students and researchers interested in geometric group theory.
Table of Contents
- Chapter A. Construction of finitary PL-homeomorphisms
- Chapter B. Generating sets
- Chapter C. The subgroup of bounded homeomorphisms $B$
- Chapter D. Presentations
- Chapter E. Isomorphisms and automorphism groups