论文标题
De Rham和Dolbeault复合物的衍生热量渐近渐近物
Derived heat trace asymptotics for the de Rham and Dolbeault complexes
论文作者
论文摘要
我们检查了对广义的witten扰动的真实和复杂设置中的衍生热量渐近造型。如果尺寸甚至是实际的上下文，我们显示了派生热痕迹渐近造型的局部密度的组成部分，是基础歧管的欧拉特征的一半。在复杂的环境中，我们假设基本的几何形状是Kähler，并显示了由Dolbeault Complex定义的派生热量痕量渐近物的局部密度的组成部分，是复杂切线束和扭曲矢量束的特征数。如果实际尺寸为$ 2 $或$ 4 $，我们会确定此特征号。在真实和复杂的设置中，局部密度通过分歧项与相应的特征类别不同。
We examine the derived heat trace asymptotics in both the real and the complex settings for a generalized Witten perturbation. If the dimension is even, in the real context we show the integral of the local density for the derived heat trace asymptotics is half the Euler characteristic of the underlying manifold. In the complex context, we assume the underlying geometry is Kähler and show the integral of the local density for the derived heat trace asymptotics defined by the Dolbeault complex is a characteristic number of the complex tangent bundle and the twisting vector bundle. We identify this characteristic number if the real dimension is $2$ or $4$. In both the real and complex settings, the local density differs from the corresponding characteristic class by a divergence term.
