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Casson, Andrew J. [VerfasserIn] ; Sullivan, Dennis [Sonstige Person, Familie und Körperschaft]; Armstrong, Mark A. [Sonstige Person, Familie und Körperschaft]; Rourke, C. P. [Sonstige Person, Familie und Körperschaft]; Cooke, George E. [Sonstige Person, Familie und Körperschaft]; Ranicki, Andrew [HerausgeberIn]

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

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  • Medientyp: E-Book
  • Titel: The Hauptvermutung Book : A Collection of Papers of the Topology of Manifolds
  • Beteiligte: Casson, Andrew J. [VerfasserIn]; Sullivan, Dennis [Sonstige Person, Familie und Körperschaft]; Armstrong, Mark A. [Sonstige Person, Familie und Körperschaft]; Rourke, C. P. [Sonstige Person, Familie und Körperschaft]; Cooke, George E. [Sonstige Person, Familie und Körperschaft]; Ranicki, Andrew [Hrsg.]
  • Erschienen: Dordrecht: Springer, 1996
  • Erschienen in: K-Monographs in Mathematics ; 1
    SpringerLink ; Bücher
    Springer eBook Collection ; Mathematics and Statistics
  • Umfang: Online-Ressource (VI, 191 p, online resource)
  • Sprache: Englisch
  • DOI: 10.1007/978-94-017-3343-4
  • ISBN: 9789401733434
  • Identifikator:
  • Schlagwörter: Global analysis ; Global differential geometry ; Cell aggregation Mathematics ; Mathematics ; Geometry ; Algebraic topology ; Manifolds (Mathematics). ; Global analysis (Mathematics). ; Geometry, Differential.
  • Entstehung:
  • Anmerkungen:
  • Beschreibung: 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