On groups of PL-homeomorphisms of the real line - Bieri, Robert; Strebel, Ralph (Providence : American Mathematical Society, 2016)
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.
* 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.
Includes bibliographical references and index.
Keywords: Homeomorphisms; Geometric group theory; Real numbers; Dimension theory (Algebra)