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:
    title: Rational Homotopy Theory and Differential Forms
  name:
    name part: Griffiths, Phillip.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Morgan, John.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2013
    edition: 2nd ed. 2013.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XI, 227 p. 46 illus. online resource.
  abstract: “Rational homotopy theory is today one of the major trends in algebraic topology. Despite the great progress made in only a few years, a textbook properly devoted to this subject still was lacking until now… The appearance of the text in book form is highly welcome, since it will satisfy the need of many interested people. Moreover, it contains an approach and point of view that do not appear explicitly in the current literature.” —Zentralblatt MATH (Review of First Edition) “The monograph is intended as an introduction to the theory of minimal models. Anyone who wishes to learn about the theory will find this book a very helpful and enlightening one. There are plenty of examples, illustrations, diagrams and exercises. The material is developed with patience and clarity. Efforts are made to avoid generalities and technicalities that may distract the reader or obscure the main theme. The theory and its power are elegantly presented. This is an excellent monograph.” —Bulletin of the American Mathematical Society (Review of First Edition) This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplical complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented. New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma *Presentation of a natural proof of a Serre spectral sequence result *Updated content throughout the book, reflecting advances in the area of homotopy theory With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differe…
  table of contents: 1 Introduction -- 2 Basic Concepts -- 3 CW Homology Theorem -- 4 The Whitehead Theorem and the Hurewicz Theorem.- 5 Spectral Sequence of a Fibration -- 6 Obstruction Theory -- 7 Eilenberg-MacLane Spaces, Cohomology, and Principal Fibrations -- 8 Postnikov Towers and Rational Homotopy Theory -- 9 deRham's theorem for simplicial complexes -- 10 Differential Graded Algebras -- 11 Homotopy Theory of DGAs -- 12 DGAs and Rational Homotopy Theory -- 13 The Fundamental Group -- 14 Examples and Computations -- 15 Functorality -- 16 The Hirsch Lemma -- 17 Quillen's work on Rational Homotopy Theory -- 18 A1-structures and C1-structures -- 19 Exercises.
  note: by Phillip Griffiths, John Morgan.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Category theory (Mathematics)
  subject:
    topic: Homological algebra
  subject:
    topic: Commutative algebra
  subject:
    topic: Commutative rings
  subject:
    topic: Topology
  subject:
    topic: Algebraic topology
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic Topology
  subject:
    topic: Category Theory, Homological Algebra
  subject:
    topic: Commutative Rings and Algebras
  subject:
    topic: Topology
  subject:
    topic: Algebra
  classification: QA612-612.8
  classification: 514.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Progress in Mathematics, 16
  identifier: 9781461484684
  identifier: http://dx.doi.org/10.1007/978-1-4614-8468-4
  record info:
    record creation date: 131002
    record change date: 20151204141159.0
    record identifier: 978-1-4614-8468-4