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The Cayley transform in complex, real and graded K-theory
International Journal of Mathematics ( IF 0.6 ) Pub Date : 2020-05-28 , DOI: 10.1142/s0129167x20500743
Chris Bourne 1, 2 , Johannes Kellendonk 3 , Adam Rennie 4
Affiliation  

We use the Cayley transform to provide an explicit isomorphism at the level of cycles from van Daele [Formula: see text]-theory to [Formula: see text]-theory for graded [Formula: see text]-algebras with a real structure. Isomorphisms between [Formula: see text]-theory and complex or real [Formula: see text]-theory for ungraded [Formula: see text]-algebras are a special case of this map. In all cases, our map is compatible with the computational techniques required in physical and geometrical applications, in particular, index pairings and Kasparov products. We provide applications to real [Formula: see text]-theory and topological phases of matter.

中文翻译:

复数、实数和分级 K 理论中的凯莱变换

我们使用 Cayley 变换在从 van Daele [公式:见文本]-理论到 [公式:见文本]-分级[公式:见文本]-具有真实结构的代数的循环水平上提供显式同构。[公式:见文本]-理论和复数或实数 [公式:见文本]-未分级 [公式:见文本]-代数之间的同构是该映射的一个特例。在所有情况下,我们的地图都与物理和几何应用所需的计算技术兼容,特别是索引配对和 Kasparov 乘积。我们提供应用到真实的[公式:见正文]——物质的理论和拓扑相。
更新日期:2020-05-28
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