Polyhedral Subdivisions and Projections of Polytopes Jörg Rambau Dissertation (Advisor: Günter M. Ziegler, TU Berlin)

Contents

• Contents
• List of Figures
• Introduction
  • Objects of Study
    • Polyhedral Subdivisions and Triangulations
    • Projections and Subdivisions
  • Links to Other Fields
    • Computational Geometry
    • Order Theory
    • Oriented Matroid Theory
    • Combinatorial Models
    • Polynomials in Several Variables
• The Generalized Baues Conjecture
  • Introduction
  • Functions on the Chamber Complex
  • Validity in Low Codimension
  • How to Construct a Counterexample
  • An Explicit Counterexample
• Triangulations of Cyclic Polytopes
  • Introduction
  • A Combinatorial Framework for Triangulations
  • Cyclic Polytopes
  • Special Triangulations of Cyclic Polytopes
  • The Higher Stasheff-Tamari Orders
  • Shellability
  • Higher Bruhat Orders
  • The Connection between $\mathcal{B}(n-2,d-1)$ and $\mathcal{S}_1(n,d)$
• Glossary of Basic Concepts
  • Partially Ordered Sets
  • Topology
  • Polytopes
  • Polytopal and Simplicial Complexes
  • Oriented Matroids
• Notation
• Bibliography
• Index