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Homology, cohomology, and sheaf cohomology for algebraic topology, algebraic geometry, and differential geometry /

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...

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Bibliographic Details
Main Authors: Gallier, Jean H. (Author), Quaintance, Jocelyn (Author)
Format: Book
Language:English
Published: Hackensack, New Jersey : World Scientific Publishing Company, [2022].
Subjects:
Homology theory.
Sheaf theory.
Algebraic topology.
Geometry, Algebraic.
Geometry, Differential.
Table of Contents:
  • Homology and cohomology
  • De Rham cohomology
  • Singular homology and cohomology
  • Simplicial homology and cohomology
  • Homology and cohomology of CW complexes
  • PoincarĂ© 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.