与R的$C^*$交叉积的边界映射及其在量子霍尔效应中的应用
Boundary maps for $C^*$-crossed products with R with an application to the quantum Hall effect
摘要：
在K-理论中，由R的交叉积代数的Wiener-Hopf扩张所产生的边界映射是Connes-Thom同构。在这篇文章中，WienerHopf扩张与海森堡群代数相结合，提供了一个相应的映射高迹（和循环上同调）的初等结构。然后直接从非交换的Stokes定理得出这个映射是对偶的w.r.t.Connes的循环上同调与K-理论的配对。作为应用，我们证明了用连续磁薛定谔算符描述的整数量子霍尔效应的量子化体电导率和量子化边电导率相等。
英文摘要：
The boundary map in K-theory arising from the Wiener-Hopf extension of a crossed product algebra with R is the Connes-Thom isomorphism. In this article the Wiener Hopf extension is combined with the Heisenberg group algebra to provide an elementary construction of a corresponding map on higher traces (and cyclic cohomology). It then follows directly from a non-commutative Stokes theorem that this map is dual w.r.t.Connes' pairing of cyclic cohomology with K-theory. As an application, we prove equality of quantized bulk and edge conductivities for the integer quantum Hall effect described by continuous magnetic Schroedinger operators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
