arXiv 1002.00532010-02math.KTmath.OA

配对的代数K理论不变性结果

Invariance results for pairings with algebraic K-theory

Jens Kaad

摘要：

对于复数上的每个代数，我们以逆变函子的方式将一列阿贝尔群联系起来。在（m-1）阶上，我们得到了代数模稳定的m-可和扰动上的m-可和Fredholm模.这些新的可重和的K-同调群与循环同调和代数K理论配对。在循环同调的情况下，配对由Chern-Connes特征诱导。由Connes-Karoubi乘法特征标导出了代数K理论与可积可和K同调之间的配对关系。

英文摘要：

To each algebra over the complex numbers we associate a sequence of abelian groups in a contravariant functorial way. In degree (m-1) we have the m-summable Fredholm modules over the algebra modulo stable m-summable perturbations. These new finitely summable K-homology groups pair with cyclic homology and algebraic K-theory. In the case of cyclic homology the pairing is induced by the Chern-Connes character. The pairing between algebraic K-theory and finitely summable K-homology is induced by the Connes-Karoubi multiplicative character.

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