Georgia Institute of Technology College of Sciences

All 3-manifolds can be described as surgery on links in the three-sphere by the celebrated theorem of Lickorish and Wallace. Motivated by the L-space conjecture, it is interesting to understand what surgery manifolds are L-spaces, which have the simplest possible Floer homology such as lens spaces. In this talk, we concentrate on surgeries on a family of links, which are called L-space links, and show possible L-space surgeries on such links. We also give some link detection results in terms of the surgeries.