Piecewise Linear Structures on Topological Manifolds

The study of triangulations of topological spaces has always been at the root of geometric topology. Among the most studied triangulations are piecewise linear triangulations of high-dimensional topological manifolds. Their study culminated in the late 1960s–early 1970s in a complete classification in the work of Kirby and Siebenmann. It is this classification that we discuss in this book, including the celebrated Hauptvermutung and Triangulation Conjecture.

The goal of this book is to provide a readable and well-organized exposition of the subject, which would be suitable for advanced graduate students in topology. An exposition like this is currently lacking.

Contents:

• Preface
• Introduction
• Graph
• Architecture of the Proof
• Normal Invariant
• Applications and Consequences of the Main Theorem
• Appendix: Quinn's Proof of Product Structure Theorem

Readership: Researchers working in manifolds, algebraic topology, and K-theory.
Key Features:

• First systematic treatment of the subject
• New treatment of certain topics