The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds by Andrew RanickiThe Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds by Andrew Ranicki

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

byAndrew Ranicki, A.J. CassonEditorAndrew Ranicki

Paperback | December 8, 2010

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The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. This 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 further 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. Then, the development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960s. Up to now, the published record of the Hauptvermutung has been incomplete. This volume brings together the original papers of Casson and Sullivan (1967), and the `Princeton Notes on the Hauptvermutung' of Armstrong, Rourke and Cooke (1968/1972). They include several results which have become part of mathematical folklore, but of which proofs had never been published. The material is complemented by an introduction on the Hauptvermutung and an account of recent developments in the area. Also, references have been updated wherever possible. Audience: This book will be valuable to all mathematicians interested in the topology of manifolds, geometry, and differential geometry.
Title:The Hauptvermutung Book: A Collection of Papers on the Topology of ManifoldsFormat:PaperbackDimensions:197 pages, 9.45 × 6.3 × 0.07 inPublished:December 8, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048147352

ISBN - 13:9789048147359

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Table of Contents

Preface. On the Hauptvermutung; A.A. Ranicki. Generalisations and Applications of Block Bundles; A.J. Casson. Triangulating Homotopy Equivalences and Homeomorphisms. Geometric Topology Seminar Notes; D.P. Sullivan. The Princeton Notes on the Hauptvermutung; M.A. Armstrong, et al. I. The Hauptvermutung According to Lashof and Rothenberg; M.A. Armstrong. II. The Hauptvermutung According to Casson and Sullivan; C.P. Rourke. III. The Hauptvermutung According to Casson and Sullivan; G.E. Cooke. Coda: Connection with the Results of Kirby and Siebenmann; C.P. Rourke.

Editorial 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)