Complete description
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.
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General info
Publisher & Imprint:
Springer
Edition details
1st ed. Softcover of orig. ed. 1996
City:
Dordrecht
Pages:
197
More info:
height 234 mm
width 156 mm
weight 288 gr
thickness 10 mm
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Age recommended:
Professional and scholarly
Subject Indexing & Classification
Dewey:(DC22) 514.223
Departments:
Analytic geometry; Differential & riemannian geometry; Algebraic topology; Infinite series;
Record updated at:
05 April, 2013
time:
21:19
Summary
The Hauptvermutung Book
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.
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