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

University Of Rochester, Rochester NY

Investigators

Abstract

0340575 Cohen The 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.