Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry
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A01=Jean H Gallier
A01=Jocelyn Quaintance
Alexander-Lefschetz Duality
Alexander-spanier Cohomology
Author_Jean H Gallier
Author_Jocelyn Quaintance
Category=PBMW
Cech Cohomology
Cellular Cohomology
Cellular Homology
Chain Complexes
De Rham Cohomology
Derived Functors
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exact Sequences
Homological Algebra
Poincare Duality
Sheaf Cohomology
Sheaves
Simplicial Homology
Singular Cohomology
Singular Homology
Spectral Sequences
Universal Delta Functors
Product details
- ISBN 9789811245022
- Publication Date: 22 Feb 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
