Basic Bundle Theory and K-Cohomology Invariants
Basic Bundle Theory and K-Cohomology Invariants
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基本丛理论和 K-上同调不变量
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
M. Schottenloher
中科院分区：
文献类型：
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作者：
D. Husemoller;M. Joachim;B. Jurčo;M. Schottenloher
d膜的k理论分类的物理背景：介绍和参考文献。- d膜的k -理论分类的物理背景：介绍和参考文献。-空间上的束和代数上的模块。- bundle和Categories的概括性。-矢量束。-向量束、射影模和幂等之间的关系。-向量束、模和幂等的k理论。纤维束的主束和节：结构和规范群的约简I.束的同伦分类和上同调：分类空间-映射的同伦类和同伦群。- Milnor构造：主束的同伦分类。-纤维束：II类规。作为同伦类的上同调类：cw -配合物。-基本特征类。-流形的特征类。-自旋结构。- k理论和博特周期性的版本。—g空间、g束、g向量束。-等变k -理论函子KG：周期性、同构性、局域化和补全。- Bott周期性映射和Clifford代数。- Gram-Schmidt过程，Iwasawa分解和主束结构约简。拓扑代数：g -等价和kk理论。-代数束：扭曲k理论。-算子代数束的同构分类。-矩阵代数束和k群的Brauer群。-扭曲k理论的解析定义。- k理论中的Atiyah-Hirzebruch谱序列。-扭曲等变k理论与Verlinde代数。- Gerbes和三维积分上同调类。——布Bundle Gerbes。-类别对象和组id Gerbes。-堆栈和Gerbes。——错误。
Physical Background to the K-Theory Classification of D-Branes: Introduction and References.- Physical Background to the K-Theory Classification of D-Branes: Introduction and References.- Bundles over a Space and Modules over an Algebra.- Generalities on Bundles and Categories.- Vector Bundles.- Relation Between Vector Bundles, Projective Modules, and Idempotents.- K-Theory of Vector Bundles, of Modules, and of Idempotents.- Principal Bundles and Sections of Fibre Bundles: Reduction of the Structure and the Gauge Group I.- Homotopy Classification of Bundles and Cohomology: Classifying Spaces.- Homotopy Classes of Maps and the Homotopy Groups.- The Milnor Construction: Homotopy Classification of Principal Bundles.- Fibrations and Bundles: Gauge Group II.- Cohomology Classes as Homotopy Classes: CW-Complexes.- Basic Characteristic Classes.- Characteristic Classes of Manifolds.- Spin Structures.- Versions of K-Theory and Bott Periodicity.- G-Spaces, G-Bundles, and G-Vector Bundles.- Equivariant K-Theory Functor KG : Periodicity, Thom Isomorphism, Localization, and Completion.- Bott Periodicity Maps and Clifford Algebras.- Gram-Schmidt Process, Iwasawa Decomposition, and Reduction of Structure in Principal Bundles.- Topological Algebras: G-Equivariance and KK-Theory.- Algebra Bundles: Twisted K-Theory.- Isomorphism Classification of Operator Algebra Bundles.- Brauer Group of Matrix Algebra Bundles and K-Groups.- Analytic Definition of Twisted K-Theory.- The Atiyah-Hirzebruch Spectral Sequence in K-Theory.- Twisted Equivariant K-Theory and the Verlinde Algebra.- Gerbes and the Three Dimensional Integral Cohomology Classes.- Bundle Gerbes.- Category Objects and Groupoid Gerbes.- Stacks and Gerbes.- Erratum.