UID:
almahu_9949461098802882
Format:
1 online resource (V, 170 p.)
Edition:
Translated from the German original "Topologie II: Algebraische Topologie". Reprint 2020
ISBN:
9783112318522
,
9783110635881
Note:
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
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DGBA Mathematics - 〈1990, De Gruyter, 9783110635881
Additional Edition:
ISBN 9783112307250
Language:
English
DOI:
10.1515/9783112318522
URL:
https://doi.org/10.1515/9783112318522
URL:
https://www.degruyter.com/isbn/9783112318522
URL:
https://www.degruyter.com/isbn/9783112318522