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OverviewThe 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. 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. Full Product DetailsAuthor: A.A. Ranicki , A.A. Ranicki , A.J. Casson , D.P. SullivanPublisher: Springer Imprint: Springer Edition: 1996 ed. Volume: 1 Dimensions: Width: 15.60cm , Height: 1.20cm , Length: 23.40cm Weight: 1.010kg ISBN: 9780792341741ISBN 10: 0792341740 Pages: 192 Publication Date: 30 September 1996 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsOn 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.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) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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