莱文编著的《代数配边理论》是一部很难得的介绍代数配边理论的专著,内容精炼简短。书中在讲述了Quillen复配边方法后,接着在固定域的光滑变量范畴上引进有向上同调理论的观点,证明了这样一个理论—范的存在性叫做代数配边。书中也包括了一些计算和应用案例。读者对象:数学专业的研究生和科研人员。
1 Cobordism and oriented cohomology
1.1 Oriented cohomology theories
1.2 Algebraic cobordism
1.3 Relations with complex cobordism
2 The definition of algebraic cobordism
2.1 Oriented Borel-Moore functors
2.2 Oriented functors of geometric type
2.3 Some elementary properties
2.4 The construction of algebraic cobordism
2.5 Some computations in algebraic cobordism
3 Fundamental properties of algebraic 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
4 Algebraic cobordism and the Lazard ring
4.1 Weak homology and Chern classes
4.2 Algebraic cobordism and K-theory
4.3 The cobordism ring of a point
4.4 Degree formulas
4.5 Comparison with the Chow groups
5 Oriented Borel-Moore homology
5.1 Oriented Borel-Moore homology theories
5.2 Other oriented theories