Applications of twisted signatures and of Khovanov homology

扭曲签名和 Khovanov 同源性的应用

• 批准号: 513007277
• 负责人: Dr. Lukas Lewark
• 金额: --
• 依托单位: Department of Mathematics
• 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/513007277?language=en
• 关键词: Applications; twisted; signatures; Khovanov; homology

This project takes place in the fields of low-dimensional topology and knot theory. Low-dimensional topology is the study of manifolds (geometric objects that locally resemble n-dimensional space) and their interrelationships in dimensions up to four, where the available toolbox is quite different from the one in higher dimensions. Knot theory is concerned with the embeddings of manifolds in one another, particularly with embeddings of a circle into three-dimensional space.The goal of this project is to apply two separate tools, both of them rather intricate and endemic to dimensions three and four, to geometric problems in knot theory. These two tools are the Casson-Gordon invariants, which are twisted signatures of metabelian coverings, and Khovanov homology, which is a categorification of the Jones polynomial.

这个项目发生在低维拓扑和结理论领域。低维拓扑是研究流形（局部类似于n维空间的几何对象）及其在四维以下的相互关系，其中可用的工具箱与高维中的工具箱有很大不同。结理论关注的是流形彼此之间的嵌入，特别是圆在三维空间中的嵌入。这个项目的目标是应用两个独立的工具，它们都是相当复杂和特有的维度3和4，在结理论的几何问题。这两种工具是卡森-戈登不变量，它是变元覆盖的扭曲签名，以及霍瓦诺夫同调，它是琼斯多项式的一种分类。