Catálogo de la biblioteca Antonio Monteiro - INMABB

Includes index.

Bibliografía: p. 728-735.

Chapter I --
Introductory Notions [1] --
1. The Fundamental Problems: Extension, Homotopy, and Classification [3] --
2. Standard Notations and Conventions [9] --
3. Maps of the n-sphere into Itself [13] --
4. Compactly Generated Spaces [17] --
5. NDR-pairs [21] --
6. Filtered Spaces [27] --
7. Fibrations [29] --
Chapter II --
CW-complexes [46] --
1. Construction of CW-complexes [48] --
2 Homology Theory of CW-complexes [54] --
3. Compression Theorems [70] --
4. Cellular Maps [76] --
5. Local Calculations [79] --
6. Regular Cell Complexes [81] --
7. Products and the Cohomology Ring [88] --
Chapter III --
Generalities on Homotopy Classes of Mappings [96] --
1. Homotopy and the Fundamental Group [98] --
2. Spaces with Base Points [102] --
3. Groups of Homotopy Classes [115] --
4 H-spaces [116] --
5. H’-spaccs [121] --
6 Exact Sequences of Mapping Functors [127] --
7. Homology Properties of H-spaces and H'-spaces [142] --
8 Hopf Algebras [149] --
Chapter IV --
Homotopy Groups [157] --
1. Relative Homotopy Groups [158] --
2. The Homotopy Sequence [161] --
3. The Operations of the Fundamental Group on the Homotopy Sequence [164] --
4. The Hurewicz Map --
5. The Eilenberg and Blakers Homology Groups [170] --
6. The Homotopy Addition Theorem [174] --
7. The Hurewicz Theorems [178] --
8. Homotopy Relations in Fibre Spaces [185] --
9. Fibrations in Which the Base or Fibre is a Sphere [194] --
10. Elementary Homotopy Theory of Lie Groups and Their Coset Spaces [196] --
Chapter V --
Homotopy Theory of CW-complexes [209] --
1. The Effect on the Homotopy Groups of a Cellular Extension [211] --
2. Spaces with Prescribed Homotopy Groups [216] --
3. Weak Homotopy Equivalence and CW-approximation [219] --
4. Aspherical Spaces [224] --
5. Obstruction Theory [228] --
6. Homotopy Extension and Classification Theorems [235] --
7. Eilenberg-Mac Lane Spaces [244] --
8. Cohomology Operations [250] --
Chapter VI --
Homology with Local Coefficients [255] --
1. Bundles of Groups [257] --
2. Homology with Local Coefficients [265] --
3. Computations and Examples [275] --
4. Local Coefficients in CW-complexes [281] --
5. Obstruction Theory in Fibre Spaces [291] --
6. The Primary Obstruction to a Lifting [297] --
7. Characteristic Classes of Vector Bundles [305] --
Chapter VII --
Homology of Fibre Spaces: Elementary Theory [314] --
I. Fibrations over « Suspension [316] --
2 The James Reduced Products [326] --
3. Further Properties of the Wang Sequence [336] --
4 Homology of the Classical Groups [341] --
5. Fibrations Having a Sphere as Fibre [349] --
6. The Homology Sequence of a Fibration [363] --
7. The Blakers Massey Homotopy Excision Theorem [366] --
Chapter VIII --
The Homology Suspension [371] --
1. The Homology Suspension [373] --
2 Proof of the Suspension Theorem [379] --
3. Applications [382] --
4. Cohomology Operations [385] --
5. Stable Operations [390] --
6. The mod 2 Steenrod Algebra [394] --
7. The Cartan Product Formula [397] --
8. Some Relations among the Steenrod Squares [403] --
9. The Action of the Steenrod Algebra on the Cohomology of Some Compact Lie Groups [408] --
Chapter IX --
Postnikov Systems [415] --
1. Connective Fibrations [417] --
2. The Postnikov Invariants of a Space [421] --
3. Amplifying a Space by a Cohomology Class [426] --
4. Reconstruction of a Space from its Postnikov System [430] --
5. Some Examples [437] --
6. Relative Postnikov Systems [443] --
7. Postnikov Systems and Obstruction Theory [449] --
Chapter X --
In Mappings into Group-like Spaces [456] --
1. The Category of a Space [457] --
2 H0-spaces [461] --
3. Nilpotency of [X, G] [462] --
4 The Case X = Xx x ••• x Xk [465] --
5. The Samelson Product [467] --
6. Commutators and Homology [470] --
7. The Whitehead Product [472] --
8. Operations in Homotopy Groups [478] --
Chapter XI --
Homotopy Operations [488] --
1. Homotopy Operations [490] --
2. The Hopf Invariant [494] --
3. The Functional Cup Product [496] --
4. The Hopf Construction invariant [502] --
5. Geometrical Interpretation of the Hop [507] --
6. The Hilton-Milnor Theorem [511] --
7. Proof of the Hilton-Milnor Theorem [515] --
8. The Hopf-Hilton Invariants [533] --
Chapter XII --
Stable Homotopy and Homology --
1. Homotopy Properties of the James Imbedding --
2. Suspension and Whitehead Products [546] --
3. The Suspension Category [550] --
4. Group Extensions and Homology [561] --
5. Stable Homotopy as a Homology Theory [571] --
6. Comparison with the Eilenberg-S teen rod Axioms [578] --
7. Cohomology Theories [594] --
Chapter XIII --
Homology of Fibre Spaces [602] --
1. The Homology of a Filtered Space [604] --
2. Exact Couples [609] --
3. The Exact Couples of a Filtered Space [613] --
4. The Spectral Sequence of a Fibration [623] --
5. Proofs of Theorems (4.7) and 4.8) [632] --
6. The Atiyah-Hirzebruch Spectral Sequence 64O --
7. The Leray-Serre Spectral Sequence [645] --
8. Multiplicative Properties of the Leray-Serre Spectral Sequence [654] --
9. Further Applications of the Leray-Serre Spectral Sequence [668] --
Appendix A --
Compact Lie Groups [673] --
1. Subgroups, Coset Spaces, Maximal Tori [674] --
2. Classifying Spaces [678] --
3. The Spinor Groups [680] --
4. The Cayley Algebra K [686] --
5. Automorphisms of K [690] --
6. The Exceptional Jordan Algebra [695] --
7. The Exceptional Lie Group [701] --
Appendix B --
Additive Relations [716] --
1. Direct Sums and Products [717] --
2. Additive Relations [722] --
Bibliography [728] --

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