A Heegaard Floer characterization of Borromean knots

Yi Ni, Caltech
Fine Hall 322

If the total rank of the knot Floer homology of a knot is equal to the total rank of the Heegaard Floer (hat) homology of the ambient 3-manifold, we say that the knot has simple knot Floer homology (or the knot is Floer simple). It is known that the unknot is the only Floer simple knot in $S3$. However, the question of determining all the Floer simple knots in general 3-manifolds is far from being solved. In this talk we will answer this question for the connected sums of $S1\times S2$: Such knots are essentially the Borromean knots.