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.