Cobordism invariance of topological edge-following states

Bulk-edge correspondence and the cobordism invariance of the index

We show that the bulk-edge correspondence for two-dimensional type A and type AII topological insulators follows directly from the cobordism invariance of the index.

On Convergence to SLE$_6$ I: Conformal Invariance for Certain Models of the Bond-Triangular Type

Following the approach outlined in [26], convergence to SLE$_6$ of the Exploration Processes for the correlated bond-triangular type models studied in [11] is established. This puts the said models in the same universality class as the standard site percolation model on the triangular lattice [27]. In the context of these models, the result is proven for all domains with boundary Minkowski dimension less than two. Moreover, the proof of convergence applies in the context of general critical 2D percolation models and for general domains, under the stipulation that Cardy's Formula can be establi…

微分方程、对偶与模不变性

Differential equations, duality and modular invariance

本文解决了由一个顶点算子代数的手征亏格零相关函数构造所有手征亏格一相关函数的问题，该顶点算子代数满足以下条件：（i）V的任何非零齐次元素的权非负，且权零子空间是一维的;（ii）每个N-分次弱V-模是完全可约的;（iii）V是C_2-上有限的。我们建立这些功能的基本属性，包括适当制定的交换性，结合性和模不变性。我们在这里开发和使用的方法与朱和其他人以前使用的方法完全不同。特别是，我们表明，$q$ -迹的产品的某些几何修改的交织算子满足模块不变系统的微分方程，对于任何固定的模块参数，减少到双周期系统只有正则奇点。本文的结果与作者在亏格为零的情况下得到的结果一起，从本质上解决了由满足上述条件的顶点算子代数的表示构造手征亏格为一的弱共形域论的问题.

Conformal Invariance for Certain Models of the Bond-Triangular Type

Following the approach outlined in [18], convergence to SLE6 of the Exploration Processes for the correlated bond-triangular type models studied in [7] is established. This puts the said models in the same universality class as the standard site percolation model on the triangular lattice [19]. The result is proven for all domains with boundary (upper) Minkowski dimension less than two. Moreover, the proof of convergence applies in the general context of critical 2D percolation models, under the stipulation that Cardy's Formula can be established.