Peter Kronheimer "Instanton homology and the Alexander polynomial." Abstract: In a 1989 paper, Andreas Floer introduced an "instanton homology" for knots in 3-manifolds. When three knots are related by skein moves, Floer showed that their instanton homology groups are related by a long exact sequence. For classical knots K, we can give Floer's instanton homology a grading, so that its graded Euler characteristic recovers the Alexander polynomial K. It is natural to conjecture that the rank of Floer's instanton homology groups of a knot K coincide with the rank of the Heegaard knot homology groups, as defined by Ozsáth-Szabó and Rasmussen.