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: Homology, cohomology, and sheaf cohomology for algebraic topology, algebraic geometry, and differential geometry
  name:
    name part: Gallier, Jean H.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Quaintance, Jocelyn
    role:
      role term: author.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: nju
    date issued: 2022
    copyright date: 2022
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xvii, 780 pages : illustrations (some color) ; 24 cm.
  abstract: For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.
  table of contents: Homology and cohomology -- De Rham cohomology -- Singular homology and cohomology -- Simplicial homology and cohomology -- Homology and cohomology of CW complexes -- Poincaré duality -- Presheaves and sheaves; Basics -- Cech cohomology with values in a presheaf -- Presheaves and sheaves; A deeper look -- Derived functors, [delta]-functors, and [del]-functors -- Universal coefficient theorems -- Cohomology of sheaves -- Alexander and Alexander-Lefschetz duality -- Spectral sequences.
  note: Jean Gallier, Jocelyn Quaintance.
  note: Includes bibliographical references and index.
  subject:
    topic: Homology theory
  subject:
    topic: Sheaf theory
  subject:
    topic: Algebraic topology
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Geometry, Differential
  classification: QA612.3 .G35 2022
  classification: 512/.64
  identifier: 9789811245022
  identifier: 9811245029
  identifier: 9789811245039
  identifier: 9789811245046
  identifier: 2021058956
  record info:
    record content source: DLC
    record creation date: 220115
    record change date: 20220824152407.7
    record identifier: in00004591334