Mathematical Sciences: Mapping Class Group & Invariants of 3-Manifolds

数学科学：映射类组

• 批准号: 9115307
• 负责人: John Harer
• 金额: $ 2.69万
• 依托单位: Washington and Lee University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1992-07-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9115307&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Mapping; Class; Group

The research project of John Harer is concerned with three major topics: The first topic is the homology of the mapping class group and related groups such as the Torelli group and the level-n mapping class groups. The second topic is the Reshetikhin-Turaev invariant of a 3- manifold and the associated representations of the mapping class groups. The third is an attempt to find an automatic structure for the mapping class group. (This is joint with S. P. Kerckhoff of Stanford University.) The study of 3-manifolds is a very natural geometric pursuit. We live in one, ignoring the time dimension, so it could even have cosmological implications.

John Harer的研究项目主要涉及三个主题：第一个主题是映射类群与相关群（如Torelli群和n级映射类群）的同调性。第二个主题是3流形的Reshetikhin-Turaev不变量和映射类群的相关表示。第三个是尝试为映射类组找到一个自动结构。（这是与斯坦福大学的S. P. Kerckhoff合作的。）对3流形的研究是一种非常自然的几何追求。我们生活在其中，忽略了时间维度，所以它甚至可能具有宇宙学意义。