Author | Spanier, Edwin H. author |
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Title | Algebraic Topology [electronic resource] / by Edwin H. Spanier |
Imprint | New York, NY : Springer New York, 1966 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9322-1 |
Descript | XIV, 548 p. online resource |
1 Set theory -- 2 General topology -- 3 Group theory -- 4 Modules -- 5 Euclidean spaces -- 1 Homotopy and The Fundamental Group -- 1 Categories -- 2 Functors -- 3 Homotopy -- 4 Retraction and deformation -- 5 H spaces -- 6 Suspension -- 7 The fundamental groupoid -- 8 The fundamental group -- Exercises -- 2 Covering Spaces and Fibrations -- 1 Covering projections -- 2 The homotopy lifting property -- 3 Relations with the fundamental group -- 4 The lifting problem -- 5 The classification of covering projections -- 6 Covering transformations -- 7 Fiber bundles -- 8 Fibrations -- Exercises -- 3 Polyhedra -- 1 Simplicial complexes -- 2 Linearity in simplicial complexes -- 3 Subdivision -- 4 Simplicial approximation -- 5 Contiguity classes -- 6 The edge-path groupoid -- 7 Graphs -- 8 Examples and applications -- Exercises -- 4 Homology -- 1 Chain complexes -- 2 Chain homotopy -- 3 The homology of simplicial complexes -- 4 Singular homology -- 5 Exactness -- 6 Mayer-Vietoris sequences -- 7 Some applications of homology -- 8 Axiomatic characterization of homology -- Exercises -- 5 Products -- 1 Homology with coefficients -- 2 The universal-coefficient theorem for homology -- 3 The Kรผnneth formula -- 4 Cohomology -- 5 The universal-coefficient theorem for cohomology -- 6 Cup and cap products -- 7 Homology of fiber bundles -- 8 The cohomology algebra -- 9 The Steenrod squaring operations -- Exercises -- 6 General Cohomology Theory and Duality -- 1 The slant product -- 2 Duality in topological manifolds -- 3 The fundamental class of a manifold -- 4 The Alexander cohomology theory -- 5 The homotopy axiom for the Alexander theory -- 6 Tautness and continuity -- 7 Presheaves -- 8 Fine presheaves -- 9 Applications of the cohomology of presheaves -- 10 Characteristic classes -- Exercises -- 7 Homotopy Theory -- 1 Exact sequences of sets of homotopy classes -- 2 Higher homotopy groups -- 3 Change of base points -- 4 The Hurewicz homomorphism -- 5 The Hurewicz isomorphism theorem -- 6 CW complexes -- 7 Homotopy functors -- 8 Weak homotopy type -- Exercises -- 8 Obstruction Theory -- 1 Eilenberg-MacLane spaces -- 2 Principal fibrations -- 3 Moore-Postnikov factorizations -- 4 Obstruction theory -- 5 The suspension map -- Exercises -- 9 Spectral Sequences and Homotopy Groups of Spheres -- 1 Spectral sequences -- 2 The spectral sequence of a fibration -- 3 Applications of the homology spectral sequence -- 4 Multiplicative properties of spectral sequences -- 5 Applications of the cohomology spectral sequence -- 6 Serre classes of abelian groups -- 7 Homotopy groups of spheres -- Exercises