PIECEWISE LINEAR STRUCTURES ON TOPOLOGICAL MANIFOLDS - Hardcover

YULI RUDYAK

9789814733786: PIECEWISE LINEAR STRUCTURES ON TOPOLOGICAL MANIFOLDS

Hardcover

ISBN 10: 9814733784 ISBN 13: 9789814733786

Verlag: World Scientific, 2016

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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.

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Rese�a del editor

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.

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