Algebraic Topology

Wolfgang Franz (Autor)

Buch | Hardcover

V, 170 Seiten

1968 | 1. Translated from the German original “Topologie II: Algebraische Topologie”. Reprint 2020
De Gruyter (Verlag)
978-3-11-230725-0 (ISBN)

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Frontmatter -- CONTENTS -- INTRODUCTION -- § 1. Analytic and Algebraic Topology -- § 2. Problems and Examples -- PART I. SIMPLICIAL COMPLEXES -- Chapter 1. GEOMETRY OF SIMPLICIAL COMPLEXES -- § 3. Hulls and Stars -- § 4. Barycentric Stars -- § 5. Simplicial Mappings -- § 6. Neighboring Mappings -- Chapter 2. HOMOLOGY GROUPS AND COHOMOLOGY GROUPS -- § 7. Orientation. Incidence Numbers -- § 8. Homology Groups -- § 9. Examples and Applications -- § 10. Cohomology Groups -- § 11. Homotopic Mappings -- PART II. CHAIN COMPLEXES AND THEIR APPLICATIONS -- Chapter 3. GENERAL THEORY -- § 12. Homology Groups of Chain Complexes -- § 13. Subcomplexes and Factor Complexes -- § 14. The Boundary Operator -- Chapter 4. FREE CHAIN COMPLEXES -- § 15. Modules and Dual Modules -- § 16. Mappings and Dual Mappings -- § 17. Free Chain Complexes. Canonical Bases -- PART III. CELL COMPLEXES. INVARIANCE -- Chapter 5. CELL COMPLEXES -- § 18. Cell Decompositions -- § 19. The Homology Groups of Cell Decompositions -- § 20. Normal Subdivisions -- Chapter 6. INVARIANCE OF THE HOMOLOGY GROUPS -- § 21. Proof of Invariance -- § 22. Supplements. Generalizations -- § 23. Results and Applications -- § 24. Local Homology Groups -- PART IV. DEVELOPMENT OF THE THEORY -- Chapter 7. PRODUCTS IN POLYHEDRA -- § 25. The Cohomology Ring -- § 26. The Cap Product -- Chapter 8. MANIFOLDS -- § 27. Definitions -- § 28. Complementary Cell Decompositions -- § 29. The Poincaré Duality Theorem -- Chapter 9. THE COHOMOLOGY RING OF A MANIFOLD -- § 30. Products in Manifolds -- § 31. Product Matrices -- BIBLIOGRAPHY -- INDEX

Frontmatter -- CONTENTS -- INTRODUCTION --
1. Analytic and Algebraic Topology --
2. Problems and Examples -- PART I. SIMPLICIAL COMPLEXES -- Chapter 1. GEOMETRY OF SIMPLICIAL COMPLEXES --
3. Hulls and Stars --
4. Barycentric Stars --
5. Simplicial Mappings --
6. Neighboring Mappings -- Chapter 2. HOMOLOGY GROUPS AND COHOMOLOGY GROUPS --
7. Orientation. Incidence Numbers --
8. Homology Groups --
9. Examples and Applications --
10. Cohomology Groups --
11. Homotopic Mappings -- PART II. CHAIN COMPLEXES AND THEIR APPLICATIONS -- Chapter 3. GENERAL THEORY --
12. Homology Groups of Chain Complexes --
13. Subcomplexes and Factor Complexes --
14. The Boundary Operator -- Chapter 4. FREE CHAIN COMPLEXES --
15. Modules and Dual Modules --
16. Mappings and Dual Mappings --
17. Free Chain Complexes. Canonical Bases -- PART III. CELL COMPLEXES. INVARIANCE -- Chapter 5. CELL COMPLEXES --
18. Cell Decompositions --
19. The Homology Groups of Cell Decompositions --
20. Normal Subdivisions -- Chapter 6. INVARIANCE OF THE HOMOLOGY GROUPS --
21. Proof of Invariance --
22. Supplements. Generalizations --
23. Results and Applications --
24. Local Homology Groups -- PART IV. DEVELOPMENT OF THE THEORY -- Chapter 7. PRODUCTS IN POLYHEDRA --
25. The Cohomology Ring --
26. The Cap Product -- Chapter 8. MANIFOLDS --
27. Definitions --
28. Complementary Cell Decompositions --
29. The Poincaré Duality Theorem -- Chapter 9. THE COHOMOLOGY RING OF A MANIFOLD --
30. Products in Manifolds --
31. Product Matrices -- BIBLIOGRAPHY -- INDEX

Erscheinungsdatum	12.03.2020
Co-Autor	Samuel D. Shore
Übersetzer	Leo F. Boron
Zusatzinfo	15 b/w ill.
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	155 x 230 mm
Gewicht	10 g
Themenwelt	Sachbuch/Ratgeber ► Natur / Technik
	Sonstiges
	Mathematik / Informatik ► Mathematik
Schlagworte	Algebra • Algebra and Number Theory • General Interest • Mathematics • Mathematik • NON-CLASSIFIABLE
ISBN-10	3-11-230725-9 / 3112307259
ISBN-13	978-3-11-230725-0 / 9783112307250
Zustand	Neuware