Topological methods in enumerative geometry of G2 manifolds

G2流形枚举几何中的拓扑方法

• 批准号: 516388824
• 负责人: Professor Dr. Sebastian Goette
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/516388824?language=en
• 关键词: Topological; methods; enumerative; geometry; G2

We propose to study a weak, homotopy-theoretical notion of associative submanifolds in G2 manifolds. This will allow us to apply powerful tools from algebraic topology, by-passing the substantial analytic difficulties one typically encounters in calibrated geometry. We will also study a comparison map relating a certain space of associative submanifolds for all G2-metrics in a given homotopy class of G2-structures to the space of homotopy-theoretic associatives. From this, we expect to gain new insights into existence and counting questions for associatives.

我们提出研究G2流形中结合子流形的一个弱同伦理论概念。这将使我们能够应用强大的工具，从代数拓扑，绕过大量的分析困难，通常会遇到校准几何。我们还将研究一个比较映射，它将一个给定的G2-结构同伦类中所有G2-度量的结合子流形空间与同伦理论结合子空间联系起来。由此，我们期望能对关联词的存在问题和计数问题有新的认识。