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

这个为期三年的美法数学合作研究项目的目标是发展代数拓扑和低维拓扑之间的联系。美国和法国的研究人员，分别由罗切斯特大学的Frederick Cohen和蒙伯利埃第二大学的Alain breugieres领导，将举行年度会议，就拓扑中的以下主题进行合作：结结构的空间；Vassiliev谱序列与Vassiliev不变量、串模编织群构型空间及其相关问题同伦量子场论；三维流形上平面连接不变量的构造从代数拓扑学的角度用范畴方法研究了三维流形的量子不变量。该项目利用了美国和法国团队的互补专业知识，并将推进对代数拓扑、同伦理论和低维拓扑的理解。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团队访问法国提供资金，法国国家科学研究中心将支付法国团队访问美国的费用。

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.