A Heegaard Floer characterization of Borromean knots
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 3manifold, 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 3manifolds 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.