Topology and K-Theory

Table of Contents

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   Book Overview
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   Chapter 1 Group Extensions and Cohomology
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   Chapter 2 Categories and Their Nerves
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   Chapter 3 Simplicial Objects
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   Chapter 4 Normalization and Conical Contractibility
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   Chapter 5 Effaceable $$\delta $$ δ -Functors
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   Chapter 6 (Co)homology of Cyclic Groups
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   Chapter 7 An Application to the Schur–Zassenhaus Theorem
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   Chapter 8 The Yoneda Lemma
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    Chapter 9 Kan Formulae
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    Chapter 10 Abelian and Additive Categories
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    Chapter 11 Diagram Chasing in Abelian Categories
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    Chapter 12 Fibered and Cofibered Categories
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    Chapter 13 Examples of Fibered Categories
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    Chapter 14 Projective Resolutions
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    Chapter 15 Analogues of Homotopy Liftings
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    Chapter 16 The Mapping Cylinder and Mapping Cone
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    Chapter 17 Derived Categories
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    Chapter 18 The First Homotopy Property
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    Chapter 19 Group Completions and Grothendieck Groups
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    Chapter 20 Devissage and Resolution Theorems
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    Chapter 21 Exact Sequences of Homotopy Classes
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    Chapter 22 Spectral Sequences
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    Chapter 23 Spectral Sequences Continued
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    Chapter 24 Hyper-Homology Spectral Sequences
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    Chapter 25 Generalized Kan Formulae
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    Chapter 26 The Hochschild–Serre Spectral Sequence
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    Chapter 27 Resolution for Exact Categories
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    Chapter 28 K $$_0$$ 0 A   $$\cong $$ ≅   K $$_{0}$$ 0   A [ T ]
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    Chapter 29 Classifying Spaces
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    Chapter 30 Higher K -Groups
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    Chapter 31 The Category $$Q{\mathcal M}$$ Q M
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    Chapter 32 Homotopy Equivalence
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    Chapter 33 A Filtration of $$Q({\mathcal P_A)}$$ Q ( P A )
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    Chapter 34 Bi-simplicial Sets and Dold–Thom
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    Chapter 35 Homology of $$Q({\mathcal P}_A)$$ Q ( P A ) and the Tits Complex
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    Chapter 36 Long Exact Sequences of K -Groups
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    Chapter 37 Localization
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    Chapter 38 The Plus Construction, $$K_1$$ K 1 and $$K_2$$ K 2