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."

Machine generated contents note: 1.Architecture of the Proof -- 1.1.Some Definitions, Notation, and Conventions -- 1.2.Principal Fibrations -- 1.3.Preliminaries on Classifying Spaces -- 1.4.Structures on Manifolds and Bundles -- 1.5.From Manifolds to Bundles -- 1.6.Homotopy PL Structures on Tn [×] Dk -- 1.7.The Product Structure Theorem -- 1.8.Non-contractibility of TOP/PL -- 1.9.Homotopy Groups of TOP/PL -- 2.Normal Invariant -- 2.1.Preliminaries on Stable Duality -- 2.2.Thom Spaces. Proof of Theorem 1.5.6 -- 2.3.Normal Morphisms and Normal Bordisms -- 2.4.The Sullivan Map s: [M, G/PL] [→] Pdim M -- 2.5.The Homotopy Type of G/PL[2] -- 2.6.Splitting Theorems -- 2.7.Detecting Families -- 2.8.Normal Invariant of a Homeomorphism V [→] Tn [×] Sk -- 3.Applications and Consequences of the Main Theorem -- 3.1.The Space G/TOP -- 3.2.The Map a: TOP/PL [→] G/PL -- 3.3.Normal Invariant of a Homeomorphism -- 3.4.Kirby -- Siebenmann Class

Note continued: 3.5.Several Examples -- 3.6.Invariance of Characteristic Classes.