Geometric Group Theory Volume 1 [Paperback]

For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.Included in papers given at the 1991 international symposium on geometric group theory, the articles in these two volumes represent the most current thought and include contributions from many of the world's leading figures in the field.Included in papers given at the 1991 international symposium on geometric group theory, the articles in these two volumes represent the most current thought and include contributions from many of the world's leading figures in the field.These two volumes contain survey papers given at the 1991 international symposium on geometric group theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the conference, and their contributions cover a wide diversity of topics. Volume I contains reviews of such subjects as isoperimetric and isodiametric functions, geometric invariants of a groups, Brick's quasi-simple filtrations for groups and 3-manifolds, string rewriting, and algebraic proof of the torus theorem, the classification of groups acting freely on R-trees, and much more. Volume II consists solely of a ground breaking paper by M. Gromov on finitely generated groups.1. Group actions and Riemann surfaces; 2. The virtual cohomological dimension of Coxeter groups; 3. The geometric invariants of a group - a survey with emphasis on the homological approach; 4. String rewriting - a survey for group theorists; 5. One-relator products with high powered relators; 6. An inaccessible group; 7. Isoperimetric and isodiametric functions - a survey; 8. On Hilbert's metric for simplices; 9. Software for axiomatic groups, isomorphism testing and finitely presented groups; 10. Proving certain groups infinite; 11. Some applications of small cancellation theory to one-relator groups and one-relator products; 12. A group theoretic proof of the torus thlÓQ