Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88
Title | Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 PDF eBook |
Author | Robion C. Kirby |
Publisher | Princeton University Press |
Pages | 368 |
Release | 2016-03-02 |
Genre | Mathematics |
ISBN | 1400881501 |
Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
Foundational Essays on Topological Manifolds, Smoothings, and Triangulations
Title | Foundational Essays on Topological Manifolds, Smoothings, and Triangulations PDF eBook |
Author | Robion C. Kirby |
Publisher | Annals of Mathematics Studies |
Pages | 355 |
Release | 1977 |
Genre | Mathematics |
ISBN | 9780691081908 |
Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
Essays on Topological Manifolds Smoothings and Triangulations
Title | Essays on Topological Manifolds Smoothings and Triangulations PDF eBook |
Author | R.C. Kirby |
Publisher | |
Pages | |
Release | 1977 |
Genre | |
ISBN |
Foundational essays on topological manifolds, smoothings, and trianguletions
Title | Foundational essays on topological manifolds, smoothings, and trianguletions PDF eBook |
Author | Robion C. Kirby |
Publisher | |
Pages | |
Release | 1977 |
Genre | |
ISBN |
Essays on Topological Manifolds Smoothings and Triangulations
Title | Essays on Topological Manifolds Smoothings and Triangulations PDF eBook |
Author | Robion C. Kirby |
Publisher | |
Pages | 12 |
Release | 1972 |
Genre | |
ISBN |
Founational Essays on Topological Manifolds, Smoothings, and Triangulations
Title | Founational Essays on Topological Manifolds, Smoothings, and Triangulations PDF eBook |
Author | Robion C. Kirby |
Publisher | |
Pages | 356 |
Release | 1977 |
Genre | |
ISBN |
Piecewise Linear Structures On Topological Manifolds
Title | Piecewise Linear Structures On Topological Manifolds PDF eBook |
Author | Yuli Rudyak |
Publisher | World Scientific |
Pages | 129 |
Release | 2015-12-28 |
Genre | Mathematics |
ISBN | 9814733806 |
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.