论文标题
Baum-Connes和Fourier-Mukai Transform
Baum-Connes and the Fourier-Mukai transform
论文作者
论文摘要
有限生成的自由阿贝尔群的鲍姆 - 康纳斯图是来自代数几何形状的傅立叶 - 穆凯变换的k理论类似物。我们用拓扑对应的语言描述了这种K理论变换，并用鲍姆 - 杜格拉斯共同体来计算其对（tori）的作用（Tori）（tori），表明傅立叶 - 木像变换映射了sebtorus的类别，将其映射到适当定义的双子圆环的类别。我们推断出傅立叶 - 穆凯反转公式。我们使用这些结果为免费的Abelian群体提供了鲍姆 - 康纳斯装配图的纯几何描述。
The Baum-Connes map for finitely generated free abelian groups is a K-theoretic analogue of the Fourier-Mukai transform from algebraic geometry. We describe this K-theoretic transform in the language of topological correspondences, and compute its action on K-theory (of tori) described geometrically in terms of Baum-Douglas cocycles, showing that the Fourier-Mukai transform maps the class of a subtorus to the class of a suitably defined dual torus. We deduce the Fourier-Mukai inversion formula. We use these results to give a purely geometric description of the Baum-Connes assembly map for free abelian groups.
