US-France Cooperative Research: Algebraic and Homological Methods in Low Dimensional Topology

美法合作研究：低维拓扑中的代数和同调方法

• 批准号: 0340575
• 负责人: Frederick Cohen
• 金额: --
• 依托单位: University of Rochester
• 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: 2004-02-01 至 2009-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0340575&HistoricalAwards=false
• 关键词: US; France; Cooperative; Research; Algebraic

0340575CohenThe objective of this three-year U.S.-France cooperative research project in mathematics is to develop connections between algebraic topology and low-dimensional topology. U.S. and French researchers, led respectively by Frederick Cohen of the University of Rochester and Alain Breuguieres of Universite de Montpellier II, will hold annual meetings to collaborate on the following topics in topology: space of knots structure; Vassiliev spectral sequence and Vassiliev invariants, skein-modules; braid groups configuration spaces and related questions; homotopy quantum field theory; construction of invariants of flat connections on 3 dimensional manifolds; and quantum invariants from the point of view of algebraic topology using a categorical approach for 3 dimensional manifolds.The project takes advantage of complementary expertise of the U.S. and French groups and will advance understanding in algebraic topology, homotopy theory, and low dimensional topology. The National Science Foundation (NSF) and the Centre National de la Recherche Scientifique (CNRS) jointly support the collaboration. NSF will provide funding for visits to France by the U.S. team and the CNRS covers the costs of the French team's travel to the United States.

0340575科恩这三年美国的目标-法国数学合作研究项目是发展代数拓扑和低维拓扑之间的联系。 由罗切斯特大学的Frederick Cohen和蒙彼利埃第二大学的Alain Breuguieres分别领导的美国和法国研究人员将举行年度会议，在拓扑学的下列主题上进行合作：结点结构空间; Vassiliev谱序列和Vassiliev不变量，skein模;辫子群配置空间和相关问题;同伦量子场论;三维流形上平坦联络不变量的构造;和量子不变量从代数拓扑的角度使用分类方法为三维流形。该项目利用美国和法国的互补专业知识的团体，并将推进理解代数拓扑，同伦理论，和低维拓扑。 国家科学基金会（NSF）和国家科学研究中心（CNRS）共同支持这项合作。 美国国家科学基金会将为美国研究小组访问法国提供资金，法国国家科学研究中心将承担法国研究小组访问美国的费用。