Structure of knot and link concordance

结和链接索引的结构

• 批准号: RGPIN-2015-05807
• 负责人: Powell, Mark
• 金额: $ 1.38万
• 依托单位: Université du Québec à Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635488
• 关键词: Structure; knot; link; concordance

Low dimensional topology is a fascinating subject, concerned with understanding spaces of dimension 3 and 4, much like the universe we inhabit.  I investigate the topology of 3- and 4-dimensional manifolds, in particular knot and link concordance.  This is the study of embeddings of circles in 3-space and embeddings of surfaces in 4-space.  My proposal aims to achieve a greater understanding of the structure of concordance spaces. Knot and link concordance is the key local question in the problem of embedding surfaces in 4-manifolds, which is central to attempts to classify 4-dimensional manifolds. I use principally algebraic and geometric tools, but sometimes analytic methods as well, to attack the questions.

低维拓扑学是一个引人入胜的学科，关注于理解3维和4维空间，就像我们所居住的宇宙一样。我研究了3维和4维流形的拓扑，特别是纽结和链接协调。这是对3-空间中圆的嵌入和4-空间中曲面的嵌入的研究。我的建议旨在更好地理解协调空间的结构。在4维流形中嵌入曲面的问题中，纽结和环的一致性是关键的局部问题，这是尝试对4维流形进行分类的核心问题。我主要使用代数和几何工具，但有时也使用分析方法来解决问题。