Heegaard Floer homology and fibred three-manifolds
主 题: Heegaard Floer homology and fibred three-manifolds
报告人: Dr. NI YI (Columbia University)
时 间: 2008-06-06 下午 2:00 - 3:00
地 点: 理科一号楼 1114(数学所活动)
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.
