Yi Ni (AIM/Columbia University)
Heegaard Floer homology and fibred three-manifolds
Heegaard Floer homology is a theory introduced by Ozsv'ath and Szab\'o as
an analogue to Seiberg-Witten theory. For knots in 3-manifolds, this
theory is refined to a filtered version, called knot Floer homology.
Ozsv\'ath and Szab\'o conjectured that knot Floer homology detects fibred
knots in the three-sphere. In this talk, we will discuss a proof of this
conjecture, based on the works of Paolo Ghiggini and of the speaker. In
fact, one can show that Heegaard Floer homology detects whether a
3-manifold is fibred, namely, whether it is a surface bundle over the
circle. Some applications will also be discussed.
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