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: Combinatorial algebraic topology
  name:
    name part: Kozlov, D. N. (Dmitriĭ Nikolaevich)
    role:
      role term: creator
    role:
      role term: author
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: gw
    date issued: 2008
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xix, 389 pages : illustrations ; 24 cm
  abstract: Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existing texts. In addition, several new themes, such as spectral sequences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms. The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field.
  table of contents: 1. Overture -- part I. Concepts of Algebraic Topology -- 2. Cell Complexes -- 3. Homology Groups -- 4. Concepts of Category Theory -- 5. Exact Sequences -- 6. Homotopy -- 7. Cofibrations -- 8. Principal [Gamma]-Bundles and Stiefel-Whitney Characteristic Classes -- part II. Methods of Combinatorial Algebraic Topology -- 9. Combinatorial Complexes Melange -- 10. Acyclic Categories -- 11. Discrete Morse Theory -- 12. Lexicographic Shellability -- 13. Evasiveness and Closure Operators -- 14. Colimits and Quotients -- 15. Homotopy Colimits -- 16. Spectral Sequences -- part III. Complexes of Graph Homomorphisms -- 17. Chromatic Numbers and the Kneser Conjecture -- 18. Structural Theory of Morphism Complexes -- 19. Characteristic Classes and Chromatic Numbers -- 20. Applications of Spectral Sequences to Hom Complexes.
  note: Dmitry Kozlov.
  note: Includes bibliographical references (pages 377-384) and index.
  subject:
    topic: Algebra, Homological
  subject:
    topic: Categories (Mathematics)
  subject:
    topic: Algebraic topology
  subject:
    topic: Combinatorial topology
  subject:
    topic: Algèbre homologique
  subject:
    topic: Catégories (Mathématiques)
  subject:
    topic: Topologie algébrique
  subject:
    topic: Topologie combinatoire
  subject:
    topic: Algebra, Homological
  subject:
    topic: Algebraic topology
  subject:
    topic: Categories (Mathematics)
  subject:
    topic: Combinatorial topology
  subject:
    topic: Algebraische Topologie
  subject:
    topic: Kombinatorische Topologie
  subject:
    topic: Topologie
  subject:
    topic: Algebraic topology
  subject:
    topic: Algebra, Homological
  subject:
    topic: Categories (Mathematics)
  subject:
    topic: Combinatorial topology
  subject:
    topic: Algebraische Topologie
  subject:
    topic: Kombinatorische Topologie
  classification: QA169 .K69 2008
  classification: 512/.64
  classification: SK 300
  classification: 510
  classification: MAT 550f
  classification: MAT 570f
  classification: 55U10
  related item:
    title info:
      title: Algorithms and computation in mathematics ; v. 21
  identifier: 9783540719618
  identifier: 354071961X
  identifier: 9783540730514
  identifier: 3540730516
  identifier: 9783540719625
  identifier: 3540719628
  identifier: 2007933072
  identifier: 11936756
  identifier: http://bvbr.bib-bvb.de:8991/F
  identifier: https://doi.org/10.1007/978-3-540-71962-5
  related item:
    location:
      url: http://bvbr.bib-bvb.de:8991/F
  related item:
    location:
      url: http://bvbr.bib-bvb.de:8991/F
  related item:
    location:
      url: https://doi.org/10.1007/978-3-540-71962-5
  location:
    physical location: TAG TAGC
  record info:
    record content source: DLC
    record creation date: 070717
    record change date: 20240807190502.9
    record identifier: in00004810766
    language of cataloging:
      language term: eng