代数配边理论（英文版）
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代数配边理论（英文版）
出版时间：2013年版
内容简介
《代数配边理论（英文版）》是一部很难得的介绍代数配边理论的专著，内容精炼简短。《代数配边理论（英文版）》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。
目录
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
出版时间：2013年版
内容简介
《代数配边理论（英文版）》是一部很难得的介绍代数配边理论的专著，内容精炼简短。《代数配边理论（英文版）》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。
目录
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