A Universal Construction for Groups Acting Freely on Real Trees

Ian Chiswell is Emeritus Professor in the School of Mathematical Sciences at Queen Mary, University of London. His main area of research is geometric group theory, especially the theory of Λ-trees. Other interests have included cohomology of groups and ordered groups. Thomas Müller is Professor in the School of Mathematical Sciences at Queen Mary, University of London. His main research interests are in geometric, combinatorial and asymptotic group theory, in algebraic combinatorics, number theory and (mostly complex) analysis.

• Preface; 1. Introduction; 2. The group RF(G); 3. The R-tree XG associated with RF(G); 4. Free R-tree actions and universality; 5. Exponent sums; 6. Functoriality; 7. Conjugacy of hyperbolic elements; 8. The centralizers of hyperbolic elements; 9. Test functions: basic theory and first applications; 10. Test functions: existence theorem and further applications; 11. A generalization to groupoids; Appendix A. The basics of Λ-trees; Appendix B. Some open problems; References; Index.