# The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra

### About this Title

**Michael Kapovich**, **Bernhard Leeb** and **John J. Millson**

Publication: Memoirs of the American Mathematical Society

Publication Year
2008: Volume 192, Number 896

ISBNs: 978-0-8218-4054-2 (print); 978-1-4704-0502-1 (online)

DOI: http://dx.doi.org/10.1090/memo/0896

MathSciNet review: 2369545

MSC: Primary 22E46; Secondary 14L24, 20E42, 20G15

### Table of Contents

**Chapters**

- 1. Introduction
- 2. Roots and Coxeter groups
- 3. The first three algebra problems and the parameter spaces $\Sigma $ for $K\backslash \bar {G}/K$
- 4. The existence of polygonal linkages and solutions to the algebra problems
- 5. Weighted configurations, stability and the relation to polygons
- 6. Polygons in Euclidean buildings and the generalized invariant factor problem
- 7. The existence of fixed vertices in buildings and computation of the saturation factors for reductive groups
- 8. The comparison of Problems Q3 and Q4