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: Sheaves in Topology
  name:
    name part: Dimca, Alexandru.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 2004
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xvi, 236 pages)
  abstract: Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties). This introduction to the subject can be regarded as a textbook on "Modern Algebraic Topology'', which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology). The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements. Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.
  table of contents: Derived Categories -- Derived Categories in Topology -- Poincaré-Verdier Duality -- Constructible Sheaves, Vanishing Cycles and Characteristic Varieties -- Perverse Sheaves -- Applications to the Geometry of Singular Spaces -- References -- Index.
  note: by Alexandru Dimca.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Differential equations, Partial
  subject:
    topic: Algebraic topology
  subject:
    topic: Algebraic topology
  subject:
    topic: Differential equations, Partial
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Mathematics
  classification: QA564-609
  classification: 516.35
  related item:
    title info:
      title: Universitext
  identifier: 9783642188688 (electronic bk.)
  identifier: 3642188680 (electronic bk.)
  identifier: 9783540206651
  identifier: 3540206655
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 121227
    record change date: 20260422202352.7
    record identifier: in00003568647
    language of cataloging:
      language term: eng