Surgery obstructions and Heegaard Floer theory
It is well known that any closed oriented 3-manifold can be obtained by surgery on a link in the 3-sphere. It is hard in general to answer: Which 3-manifolds can, or cannot, be obtained by surgery on a knot (single component link)? In this talk, we will survey results related to this question, responded by using Heegaard Floer theory. We also introduce our result on 3-manifolds with the first betti-number 1. This is a joint work with Matt Hedden and Min Hoon Kim.