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: Basic Algebraic Topology and its Applications
  name:
    name part: Adhikari, Mahima Ranjan.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ii
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXIX, 615 p. 176 illus. online resource.
  abstract: This book provides an accessible introduction to algebraic topology, a ﬁeld at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book oﬀers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.
  table of contents: Prerequisite Concepts and Notations -- Basic Homotopy -- The Fundamental Groups.-Covering Spaces -- Fibre Bundles, Vector Bundles and K-theory -- Geometry of Simplicial Complexes and Fundamental Groups -- Higher Homotopy Groups -- Products in Higher Homotopy Groups -- CW-complexes and Homotopy -- Eilenberg-MacLane Spaces -- Homology and Cohomology Theories -- Eilenberg-Steenrod Axioms for Homology and Cohomology Theories -- Consequences of the Eilenberg-Steenrod Axioms -- Some Applications of Homology Theory -- Spectral Homology and Cohomology Theories -- Obstruction Theory -- More Relations Between Homotopy and Homology Groups -- A Brief Historical Note.
  note: by Mahima Ranjan Adhikari.
  subject:
    topic: Mathematics
  subject:
    topic: Group theory
  subject:
    topic: K-theory
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: Algebraic topology
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Complex manifolds
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic Topology
  subject:
    topic: Topological Groups, Lie Groups
  subject:
    topic: Manifolds and Cell Complexes (incl. Diff.Topology)
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: K-Theory
  classification: QA612-612.8
  classification: 514.2
  related item:
    title info:
      title: Springer eBooks
  identifier: 9788132228431
  identifier: http://dx.doi.org/10.1007/978-81-322-2843-1
  record info:
    record creation date: 160916
    record change date: 20160916130958.0
    record identifier: 978-81-322-2843-1