TY  - BOOK
AU  - Bieri,Robert
AU  - Strebel,Ralph
TI  - On groups of PL-homeomorphisms of the real line
T2  - Mathematical surveys and monographs
SN  - 9781470429010 
U1  - 510MS 23
PY  - 2016///
CY  - Providence : 
PB  - American Mathematical Society
KW  - Homeomorphisms
KW  - Geometric group theory
KW  - Real numbers
KW  - Dimension theory (Algebra)
N1  - Includes bibliographical references and index; * Introduction* Construction of finitary PL-homeomorphisms* Generating sets* The subgroup of bounded homeomorphisms $B$* Presentations* Isomorphisms and automorphism groups* Notes* Bibliography* Index of notation* Subject index.
N2  - 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
ER  -