rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: A
    title: History of Algebraic and Differential Topology, 1900 - 1960
  name:
    name part: Dieudonné, Jean.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXII, 648 p. online resource.
  abstract: Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions. ***************************** This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet [The author] traces the development of algebraic and differential topology from the innovative work by Poincaré at the turn of the century to the period around 1960. [He] has given a superb account of the growth of these fields.… The details are interwoven with the narrative in a very pleasant fashion.… [The author] has previous written histories of functional analysis and of algebraic geometry, but neither book was on such a grand scale as this one. He has made it possible to trace the important steps in the growth of algebraic and differential topology, and to admire the hard work and major advances made by the founders. —Zentralblatt MATH.
  table of contents: Simplicia1 Techniques and Homology -- The Work of Poincar#x00E9; -- The Build-Up of #x201C;Classical#x201D; Homology -- The Beginnings of Differential Topology -- The Various Homology and Cohomology Theories -- The First Applications of Simplicia1 Methods and of Homology -- The Concept of Degree -- Dimension Theory and Separation Theorems -- Fixed Points -- Local Homological Properties -- Quotient Spaces and Their Homology -- Homolagy of Groups and Homogeneous Spaces -- Applications of Homology to Geometry and Analysis -- Homotopy and its Relution to Homology -- Fundamental Group and Covering Spaces -- Elementary Notions and Early Results in Homotopy Theory -- Fibrations -- Homology of Fibrations -- Sophisticated Relations between Homotopy and Homology -- Cohomology Operations -- Generalized Homology and Cohomology.
  note: by Jean Dieudonné.
  subject:
    topic: Mathematics
  subject:
    topic: Differential geometry
  subject:
    topic: History
  subject:
    topic: Algebraic topology
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic Topology
  subject:
    topic: Differential Geometry
  subject:
    topic: History of Mathematical Sciences
  classification: QA612-612.8
  classification: 514.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Modern Birkhäuser Classics
  identifier: 9780817649074
  identifier: http://dx.doi.org/10.1007/978-0-8176-4907-4
  record info:
    record creation date: 100301
    record change date: 20160526064649.0
    record identifier: 978-0-8176-4907-4