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Lectures on algebraic topology

Author: Albrecht Dold
Publisher: Berlin : Springer-Verlag, 1995.
Series: Classics in mathematics
Edition/Format:   Print book : English : 2nd edView all editions and formats

Suitable for younger generations of students and researchers, this title deals with higher mathematics.


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Document Type: Book
All Authors / Contributors: Albrecht Dold
ISBN: 3540586601 9783540586609
OCLC Number: 468815757
Notes: Précédemment paru dans la collection : "Grundlehren der mathematischen Wissenschaften", vol. 200, 1980.
Bibliogr. p. 368-370. Index.
Description: XI-377 p. : ill. ; 24 cm.
Contents: I Preliminaries on Categories, Abelian Groups, and Homotopy.- x1 Categories and Functors.- x2 Abelian Groups (Exactness, Direct Sums, Free Abelian Groups).- x3 Homotopy.- II Homology of Complexes.- x1 Complexes.- x2 Connecting Homomorphism, Exact Homology Sequence.- x3 Chain-Homotopy.- x4 Free Complexes.- III Singular Homology.- x1 Standard Simplices and Their Linear Maps.- x2 The Singular Complex.- x3 Singular Homology.- x4 Special Cases.- x5 Invariance under Homotopy.- x6 Barycentric Subdivision.- x7 Small Simplices. Excision.- x8 Mayer-Vietoris Sequences.- IV Applications to Euclidean Space.- x1 Standard Maps between Cells and Spheres.- x2 Homology of Cells and Spheres.- x3 Local Homology.- x4 The Degree of a Map.- x5 Local Degrees.- x6 Homology Properties of Neighborhood Retracts in ?n.- x7 Jordan Theorem, Invariance of Domain.- x8 Euclidean Neighborhood Retracts (ENRs).- V Cellular Decomposition and Cellular Homology.- x1 Cellular Spaces.- x2 CW-Spaces.- x3 Examples.- x4 Homology Properties of CW-Spaces.- x5 The Euler-Poincare Characteristic.- x6 Description of Cellular Chain Maps and of the Cellular Boundary Homomorphism.- x7 Simplicial Spaces.- x8 Simplicial Homology.- VI Functors of Complexes.- x1 Modules.- x2 Additive Functors.- x3 Derived Functors.- x4 Universal Coefficient Formula.- x5 Tensor and Torsion Products.- x6 Horn and Ext.- x7 Singular Homology and Cohomology with General Coefficient Groups.- x8 Tensorproduct and Bilinearity.- x9 Tensorproduct of Complexes. Kunneth Formula.- x10 Horn of Complexes. Homotopy Classification of Chain Maps.- x11 Acyclic Models.- x12 The Eilenberg-Zilber Theorem. Kunneth Formulas for Spaces.- VII Products.- x1 The Scalar Product.- x2 The Exterior Homology Product.- x 3 The Interior Homology Product (Pontijagin Product).- x 4 Intersection Numbers in ?n.- x5 The Fixed Point Index.- x6 The Lefschetz-Hopf Fixed Point Theorem.- x7 The Exterior Cohomology Product.- x 8 The Interior Cohomology Product (?-Product).- x 9 ?-Products in Projective Spaces. Hopf Maps and Hopf Invariant.- x10 Hopf Algebras.- x11 The Cohomology Slant Product.- x12 The Cap-Product (?-Product).- x 13 The Homology Slant Product, and the Pontijagin Slant Product.- VIII Manifolds.- x1 Elementary Properties of Manifolds.- x2 The Orientation Bundle of a Manifold.- x3 Homology of Dimensions ? n in n-Manifolds.- x4 Fundamental Class and Degree.- x5 Limits.- x6 ?ech Cohomology of Locally Compact Subsets of ?n.- x7 Poincare-Lefschetz Duality.- x8 Examples, Applications.- x9 Duality in ?-Manifolds.- x10 Transfer.- x11 Thom Class, Thom Isomorphism.- x12 The Gysin Sequence. Examples.- x13 Intersection of Homology Classes.- Appendix: Kan- and ?ech-Extensions of Functors.- x1 Limits of Functors.- x2 Polyhedrons under a Space, and Partitions of Unity.- x3 Extending Functors from Polyhedrons to More General Spaces.
Series Title: Classics in mathematics
Responsibility: Albrecht Dold.
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