Invariants of Links and 3-manifolds

链接和 3 流形的不变量

• 批准号: 0437552
• 负责人: Thang Le
• 金额: $ 8.08万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-03-22 至 2006-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0437552&HistoricalAwards=false
• 关键词: Invariants; Links; manifolds

DMS-0204158Thang LeThang Le plans to continue his study of quantum and finite typeinvariants of links and 3-manifolds. In particular, he would liketo study problems arising around the volume conjecture whichconnects quantum invariants to classical objects like fundamentalgroups, torsions, and volumes. Other problems involve integralityproperties (in broad sense) of quantum invariants and thetopology behind them, and their applications. The field hasinteractions with geometry, combinatorics, number theory, andphysics.The theory of knots and 3-manifolds is an old branch ofmathematics which has gained renewed interest amongmathematicians and physicists after the discovery of the Jonespolynomial and its relation to theoretical physics (quantum fieldtheory, high energy physics). In fact, it is now one of the mostactive domains in mathematics. Many results of knot theory mayalso find applications in molecular biology. To classify knotsand 3-manifolds, mathematicians use "invariants". This researchproject studies new classes of invariants of knots and3-manifolds and their relationships with the classical ones. Thenew invariants are very powerful in distinguishing knots and3-manifolds.

DMS-0204158Thang Lethang Le计划继续研究链接和3个manifolds的量子和有限类型。特别是，他会研究围绕体积猜想引起的问题，这些猜想会将量子不变性与基本群，扭转和体积等经典对象相关联。其他问题涉及量子不变的和thetopology的完整性普遍性以及它们的应用。田野与几何形状，组合学，数理论和植物学的交流。实际上，它现在是数学中最活跃的领域之一。结理论的许多结果发现在分子生物学中的应用。为了对打结进行分类，数学家使用“不变”。这项研究项目研究了结的新类别和3个manifolds的新类别及其与经典的关系。然后，不变的人在区分结和3个manifolds方面非常强大。