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Sheaf Theory [[electronic resource] /] / by Glen E. Bredon
| Sheaf Theory [[electronic resource] /] / by Glen E. Bredon |
| Autore | Bredon Glen E |
| Edizione | [2nd ed. 1997.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1997 |
| Descrizione fisica | 1 online resource (XI, 504 p.) |
| Disciplina | 512 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Algebra
Algebraic topology Algebraic Topology |
| ISBN | 1-4612-0647-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Sheaves and Presheaves -- 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 -- 1 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 ?-soft and ?-fine sheaves -- 10 Subspaces -- 11 The Vietoris mapping theorem and homotopy invariance -- 12 Relative cohomology -- 13 Mayer-Vietoris theorems -- 14 Continuity -- 15 The Künneth 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 ?ech cohomology -- Exercises -- IV Applications of Spectral Sequences -- 1 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 Cartan -- 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-Moore Homology -- 1 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 Poincaré duality -- 10 The cap product -- 11 Intersection theory -- 12 Uniqueness theorems -- 31 Uniqueness theorems for maps and relative homology -- 14 The Künneth 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 ?ech Homology -- 1 Theory of cosheaves -- 2 Local triviality -- 3 Local isomorphisms -- 4 Cech homology -- 5 The reflector -- 6 Spectral sequences -- 7 Coresolutions -- 8 Relative ?ech 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 -- List of Symbols -- List of Selected Facts. |
| Record Nr. | UNINA-9910480143403321 |
Bredon Glen E
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Sheaf Theory [[electronic resource] /] / by Glen E. Bredon
| Sheaf Theory [[electronic resource] /] / by Glen E. Bredon |
| Autore | Bredon Glen E |
| Edizione | [2nd ed. 1997.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1997 |
| Descrizione fisica | 1 online resource (XI, 504 p.) |
| Disciplina | 512 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Algebra
Algebraic topology Algebraic Topology |
| ISBN | 1-4612-0647-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Sheaves and Presheaves -- 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 -- 1 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 ?-soft and ?-fine sheaves -- 10 Subspaces -- 11 The Vietoris mapping theorem and homotopy invariance -- 12 Relative cohomology -- 13 Mayer-Vietoris theorems -- 14 Continuity -- 15 The Künneth 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 ?ech cohomology -- Exercises -- IV Applications of Spectral Sequences -- 1 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 Cartan -- 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-Moore Homology -- 1 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 Poincaré duality -- 10 The cap product -- 11 Intersection theory -- 12 Uniqueness theorems -- 31 Uniqueness theorems for maps and relative homology -- 14 The Künneth 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 ?ech Homology -- 1 Theory of cosheaves -- 2 Local triviality -- 3 Local isomorphisms -- 4 Cech homology -- 5 The reflector -- 6 Spectral sequences -- 7 Coresolutions -- 8 Relative ?ech 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 -- List of Symbols -- List of Selected Facts. |
| Record Nr. | UNINA-9910789350003321 |
|
Bredon Glen E
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Sheaf Theory / / by Glen E. Bredon
| Sheaf Theory / / by Glen E. Bredon |
| Autore | Bredon Glen E |
| Edizione | [2nd ed. 1997.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1997 |
| Descrizione fisica | 1 online resource (XI, 504 p.) |
| Disciplina | 512 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Algebra
Algebraic topology Algebraic Topology |
| ISBN | 1-4612-0647-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Sheaves and Presheaves -- 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 -- 1 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 ?-soft and ?-fine sheaves -- 10 Subspaces -- 11 The Vietoris mapping theorem and homotopy invariance -- 12 Relative cohomology -- 13 Mayer-Vietoris theorems -- 14 Continuity -- 15 The Künneth 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 ?ech cohomology -- Exercises -- IV Applications of Spectral Sequences -- 1 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 Cartan -- 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-Moore Homology -- 1 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 Poincaré duality -- 10 The cap product -- 11 Intersection theory -- 12 Uniqueness theorems -- 31 Uniqueness theorems for maps and relative homology -- 14 The Künneth 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 ?ech Homology -- 1 Theory of cosheaves -- 2 Local triviality -- 3 Local isomorphisms -- 4 Cech homology -- 5 The reflector -- 6 Spectral sequences -- 7 Coresolutions -- 8 Relative ?ech 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 -- List of Symbols -- List of Selected Facts. |
| Record Nr. | UNINA-9910827770803321 |
|
Bredon Glen E
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topology and Geometry [[electronic resource] /] / by Glen E. Bredon
| Topology and Geometry [[electronic resource] /] / by Glen E. Bredon |
| Autore | Bredon Glen E |
| Edizione | [1st ed. 1993.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1993 |
| Descrizione fisica | 1 online resource (XXIII, 131 p.) |
| Disciplina | 514 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Topology
Geometry |
| ISBN | 1-4757-6848-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I General Topology -- II Differentiable Manifolds -- III Fundamental Group -- IV Homology Theory -- V Cohomology -- VI Products and Duality -- VII Homotopy Theory -- Appendices -- App. A. The Additivity Axiom -- App. B. Background in Set Theory -- App. C. Critical Values -- App. D. Direct Limits -- App. E. Euclidean Neighborhood Retracts -- Index of Symbols. |
| Record Nr. | UNINA-9910480430003321 |
|
Bredon Glen E
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topology and Geometry [[electronic resource] /] / by Glen E. Bredon
| Topology and Geometry [[electronic resource] /] / by Glen E. Bredon |
| Autore | Bredon Glen E |
| Edizione | [1st ed. 1993.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1993 |
| Descrizione fisica | 1 online resource (XXIII, 131 p.) |
| Disciplina | 514 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Topology
Geometry Topologia algebraica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 1-4757-6848-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I General Topology -- II Differentiable Manifolds -- III Fundamental Group -- IV Homology Theory -- V Cohomology -- VI Products and Duality -- VII Homotopy Theory -- Appendices -- App. A. The Additivity Axiom -- App. B. Background in Set Theory -- App. C. Critical Values -- App. D. Direct Limits -- App. E. Euclidean Neighborhood Retracts -- Index of Symbols. |
| Record Nr. | UNINA-9910792477703321 |
|
Bredon Glen E
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topology and Geometry / / by Glen E. Bredon
| Topology and Geometry / / by Glen E. Bredon |
| Autore | Bredon Glen E |
| Edizione | [1st ed. 1993.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1993 |
| Descrizione fisica | 1 online resource (XXIII, 131 p.) |
| Disciplina |
514
514.2 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Topology
Geometry Topologia algebraica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 1-4757-6848-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I General Topology -- II Differentiable Manifolds -- III Fundamental Group -- IV Homology Theory -- V Cohomology -- VI Products and Duality -- VII Homotopy Theory -- Appendices -- App. A. The Additivity Axiom -- App. B. Background in Set Theory -- App. C. Critical Values -- App. D. Direct Limits -- App. E. Euclidean Neighborhood Retracts -- Index of Symbols. |
| Record Nr. | UNINA-9910808754403321 |
|
Bredon Glen E
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||