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)
DOI: https://doi.org/10.1090/surv/215
MathSciNet review: MR3560537
MSC: Primary 20F38; Secondary 20E32, 20F05, 20F28
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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
Front/Back Matter
Chapters
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