Workshop in Knot Concordance and Homology Cobordism

Wesleyan University, Middletown CT

Investigators

Abstract

In 1957, R. H. Fox and J. Milnor introduced the seminal idea that the concordance class of the link of a singularity obstructs its removal. Both concordance of knots, and the motivating goal of understanding singularities remain central to topology and algebraic geometry. In the last 10 years we have seen tremendous advances in our knowledge of knot and link concordance. The introduction of the n-solvable filtration, by Cochran-Orr-Teichner, and the subsequent work of many authors establishing the non-triviality of (half of) the graded quotients has led to the realization that perhaps knot concordance is as fully complicated as the fundamental group might allow. A conference will be held at Wesleyan University, July 19-23, 2010, to bring together a variety of researchers and students whose work connects to knot concordance. Knot theory is the study of knotted curves in 3-space. The study of knotted curves has important applications in biology and physics. A fundamental question in knot theory and low-dimensional topology is when such a curve bounds a disk in 4-space. This motivating question is the foundation for the study of knot concordance. Knot concordance was born of the study of 4-manifolds and remains its most accessible progeny.