Yi Ni
Princeton University
Knot Floer homology detects fibred knots
Abstract: Knot Floer homology is a knot invariant introduced by Ozsv\'ath and Szab\'o, and by Rasmussen. The Euler characteristic of knot Floer homology gives rise to the Alexander polynomial of a knot, so many properties of Alexander polynomial can be generalized to knot Floer homology. For example, if a knot is fibred, then its knot Floer homology is "monic". Ozsv\'ath and Szab\'o conjectured that the converse of the previous fact is also true, namely, if the knot Floer homology is monic, then the knot is fibred. In this talk, we will discuss a proof of this conjecture, based on the works of Paolo Ghiggini and of the speaker. A corollary is that if a knot in S3 admits a lens space surgery, then the knot is fibred.