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The elementary and formal algebraic theory of multiplicative sequences is contained in § 1. In particular the Todd polynomials T i and also the polynomials L i used in the index theorem, are defined. Results on sheaves needed in the sequel are collected in § 2. The basic properties of fibre bundles are given in § 3. In § 4 these are applied to obtain characteristic classes. In particular, Chernthe classes and Pontrjaginclasses are defined. The results of § 1 are not used until § 8. The reader is therefore advised to begin with § 2 and to refer to § 1 only when necessary.
KeywordsExact Sequence Vector Bundle Fibre Bundle Complex Manifold Open Covering
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