内容

目次

Introduction.- I. Cobordism and oriented cohomology.- 1.1. Orientedcohomology theories. 1.2. Algebraic cobordism. 1.3. Relations with complexcobordism. - II. The definition of algebraic cobordism. 2.1. OrientedBorel-Moore functions. 2.2. Oriented functors of geometric type. 2.3. Someelementary properties. 2.4. The construction of algebraic cobordism. 2.5.Some computations in algebraic cobordism.- III. Fundamental properties ofalgebraic cobordism. 3.1. Divisor classes. 3.2. Localization. 3.3.Transversality. 3.4. Homotopy invariance. 3.5. The projective bundle formula.3.6. The extended homotopy property. IV. Algebraic cobordism and the Lazardring. 4.1. Weak homology and Chern classes. 4.2. Algebraic cobordism andK-theory. 4.3. The cobordism ring of a point. 4.4. Degree formulas. 4.5.Comparison with the Chow groups. V. Oriented Borel-Moore homology. 5.1.Oriented Borel-Moore homology theories. 5.2. Other oriented theories.- VI.Functoriality. 6.1. Refined cobordism. 6.2. Intersection with apseudo-divisor. 6.3. Intersection with a pseudo-divisor II. 6.4. A movinglemma. 6.5. Pull-back for l.c.i. morphisms. 6.6. Refined pull-back andrefined intersections. VII. The universality of algebraic cobordism. 7.1.Statement of results. 7.2. Pull-back in Borel-Moore homology theories. 7.3.Universality 7.4. Some applications.- Appendix A: Resolution ofsingularities.- References.- Index.- Glossary of Notation.