The Hauptvermutung book : a collection of papers of the topology of manifolds
Author(s)
Bibliographic Information
The Hauptvermutung book : a collection of papers of the topology of manifolds
(K-monographs in mathematics, v. 1)
Kluwer Academic Publishers, c1996
- Other Title
-
The Hauptvermutung book : a collection of papers on the topology of manifolds
Available at 26 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references
Description and Table of Contents
Description
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.
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.
by "Nielsen BookData"