層論（第2版）

Preface
I Sheaves and Presheaves
　1　Definitions
　2　Homomorphisms, subsheaves, and quotient sheaves
　3　Direct and inverse images
　4　Cohomomorphisms
　5　Algebraic constructions
　6　Supports
　7　Classical cohomology theories
　Exercises
II Sheaf Cohomology
　I Differential sheaves and resolutions
　2 The canonical resolution and sheaf cohomology
　3 Injective sheaves
　4 Acyclic sheaves
　5 Flabby sheaves
　6 Connected sequences of functors
　7 Axioms for cohomology and the cup product
　8 Maps of spaces
　9 φ-soft and φ-fine sheaves
　10 Subspaces
　11 The Vietoris mapping theorem and homotopy invariance
　12 Relative cohomology
　13 Mayer-Vietoris theorems
　14 Continuity
　15 The Kiinneth and universal coefficient theorems
　16 Dimension
　17 Local connectivity
　18 Change of supports; local cohomology groups
　19 The transfer homomorphism and the Smith sequences
　20 Steenrod's cyclic reduced powers
　21 The Steenrod operations
　Exercises
III Comparison with Other Cohomology Theories
　1 Singular cohomology
　2 Alexander-Spanier cohomology
　3 de Rham cohomology
　4 Cech cohomology
　Exercises
IV Applications of Spectral Sequerices
　I The spectral sequence of a differential sheaf
　2 The fundamental theorems of sheaves
　3 Direct image relative to a support family
　4 The Leray sheaf
　5 Extension of a support family by a family on the base space
　6 The Leray spectral sequence of a map
　7 Fiber bundles
　8 Dimension
　9 The spectral sequences of Borel and Caftan
　10 Characteristic classes
　11 The spectral sequence of a filtered differential sheaf
　12 The Fary spectral sequence
　13 Sphere bundles with singularities
　14 The Oliver transfer and the Conner conjecture
　Exercises
V Borel-Uoore Homology
　I Cosheaves
　2 The dual of a differential cosheaf
　3 Homology theory
　4 Maps of spaces
　5 Subspaces and relative homology
　6 The Vietoris theorem, homotopy, and covering spaces
　7 The homology sheaf of a map
　8 The basic spectral sequences
　9 Poincare duality
　10 The cap product
　11 Intersection theory
　12 Uniqueness theorems
　13 Uniqueness theorems for maps and relative homology
　14 The Kuinneth formula
　15 Change of rings
　16 Generalized manifolds
　17 Locally homogeneous spaces
　18 Homological fibrations and p-adic transformation groups
　19 The transfer homomorphism in homology
　20 Smith theory in homology
　Exercises
VI Cosheaves and Cech Homology
　I Theory of cosheaves
　2 Local triviality
　3 Local isomorphisms
　4 Cech homology
　5 The reflector
　6 Spectral sequences
　7 Coresolutions
　8 Relative Cech homology
　9 Locally paracompact spaces
　10 Borel-Moore homology
　11 Modified Borel-Moore homology
　12 Singular homology
　13 Acyclic coverings
　14 Applications to maps
　Exercises
A Spectral Sequences
　1 The spectral sequence of a filtered complex
　2 Double complexes
　3 Products
　4 Homomorphisms
B Solutions to Selected Exercises
　Solutions for Chapter I
　Solutions for Chapter II
　Solutions for Chapter III
　Solutions for Chapter IV
　Solutions for Chapter V
　Solutions for Chapter VI
Bibliography
List of Symbols
List of Selected Facts
Index