Abstract:

Heegaard Floer homology is an invariant for 3-manifolds, as well as knots and links in 3-manifolds. A classical theorem of Lickorish-Wallace states that every 3-manifold can be constructed by Dehn surgery on a link in S^3. Heegaard Floer homology admits useful Dehn surgery formulas, which have played an important role in many applications of the theory. In this talk we will describe some interesting algebraic perspectives on these formulas, as well as some applications of these perspectives.