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The Hauptvermutung Book : A Collection of Papers on the Topology of Manifolds - A. Ranicki

The Hauptvermutung Book

A Collection of Papers on the Topology of Manifolds

Hardcover Published: 30th September 1996
ISBN: 9780792341741
Number Of Pages: 192

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The Hauptvermutung is the conjecture that any two triangulations of a poly­ hedron are combinatorially equivalent. The conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that furt her development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. These polyhedra were not manifolds, leaving open the Hauptvermu­ tung for manifolds. The development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960's. Unfortunately, the published record of the manifold Hauptvermutung has been incomplete, as was forcefully pointed out by Novikov in his lecture at the Browder 60th birthday conference held at Princeton in March 1994. This volume brings together the original 1967 papers of Casson and Sulli­ van, and the 1968/1972 'Princeton notes on the Hauptvermutung' of Armstrong, Rourke and Cooke, making this work physically accessible. These papers include several other results which have become part of the folklore but of which proofs have never been published. My own contribution is intended to serve as an intro­ duction to the Hauptvermutung, and also to give an account of some more recent developments in the area. In preparing the original papers for publication, only minimal changes of punctuation etc.

Industry Reviews

` ... long awaited account of a major achievement of modern mathematics. ... highly recommended for all topologists and for those who are interested in the developments of major topological tools.'
Acta Scientificae Mathematicae, 63 (1997)

Preface
On the Hauptvermutung
Generalisations and Applications of Block Bundles
Triangulating Homotopy Equivalences and Homeomorphisms. Geometric Topology Seminar Notes
The Princeton Notes on the Hauptvermutung
I. The Hauptvermutung According to Lashof and Rothenberg
II.The Hauptvermutung according to Casson and Sullivan
III. The Hauptvermutung according to Casson and Sullivan
Coda: Connection with the results of Kirby and Siebenmann
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792341741
ISBN-10: 0792341740
Series: K-Monographs in Mathematics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 192
Published: 30th September 1996
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.27
Weight (kg): 0.46

Earn 519 Qantas Points
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