Contents
Preface ix
Acknowledgements xii
Chapter I. Projective modules and vector bundles 1
§1. Free modules, GLn, and stably free modules 1
§2. Projective modules 8
§3. The Picard group of a commutative ring 20
§4. Topological vector bundles and Chern classes 34
§5. Algebraic vector bundles 49
Chapter II. The Grothendieck group K0 69
§1. The group completion of a monoid 69
§2. K0 of a ring 74
§3. K(X), KO(X), and KU(X) of a topological space 89
§4. Lambda and Adams operations 98
§5. K0 of a symmetric monoidal category 114
§6. K0 of an abelian category 124
§7. K0 of an exact category 140
§8. K0 of schemes and varieties 157
§9. K0 of a Waldhausen category 172
Appendix. Localizing by calculus of fractions 189
Chapter III. K1 and K2 of a ring 197
§1. The Whitehead group K1 of a ring 197
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