Orbifold等价：结构和新例
Orbifold equivalence: structure and new examples
摘要：
轨道等价是一种不依赖于群作用的对称性概念。在其他应用中，它导致了迄今为止不相关的奇点之间令人惊讶的联系。虽然这个概念可以定义在一个非常一般的范畴理论的语言，我们专注于最明确的设置在矩阵因式分解，其中orbifold等价产生的缺陷具有特殊性质。例子是相对困难的建设，但我们发现一些结构特征，区分orbifold等价-最显着的有限扰动扩展。我们利用这些性质设计了一个搜索算法，然后提出了一些新的例子，包括阿诺德奇点。
英文摘要：
Orbifold equivalence is a notion of symmetry that does not rely on group actions. Among other applications, it leads to surprising connections between hitherto unrelated singularities. While the concept can be defined in a very general category-theoretic language, we focus on the most explicit setting in terms of matrix factorisations, where orbifold equivalences arise from defects with special properties. Examples are relatively difficult to construct, but we uncover some structural features that distinguish orbifold equivalences -- most notably a finite perturbation expansion. We use those properties to devise a search algorithm, then present some new examples including Arnold singularities.
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