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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)
MathSciNet review: 2369545
MSC: Primary 22E46; Secondary 14L24, 20E42, 20G15

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Table of Contents


  • 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
American Mathematical Society