模高斯曲率背后的循环结构
Cyclic Structure behind Modular Gaussian Curvature
摘要：
我们提出了一个系统的计划计算最近发展的谱几何中出现的非交换环面和$θ$ -变形黎曼流形重排算子的变化。它可以概括为一个范畴，其对象由重排算子的谱函数组成，态射由与变分学的基本运算相关的变换生成。态射的生成元满足Connes循环范畴中的大部分关系，但也包括所有的偏导数。并与Hopf循环理论作了比较。
英文摘要：
We propose a systematic scheme for computing the variation of rearrangement operators arising in the recently developed spectral geometry on noncommutative tori and $θ$-deformed Riemannian manifolds. It can be summarized as a category whose objects consists of spectral functions of the rearrangement operators and morphisms are generated by transformations associated to basic operations of the variational calculus. The generators of the morphisms fulfil most of the relations in Connes's cyclic category, but also include all the partial derivatives. Comparison with Hopf cyclic theory has also been made.
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