Floer homology
The main body of his work involves embedded contact homology, or ECH. ECH is a holomorphic curve model for the Seiberg–Witten–Floer homology of a three-manifold, and is thus a version of Taubes's Gromov invariant for certain four-manifolds with boundary. Ideas connected to ECH were important in Taubes's proof of the Weinstein conjecture for three-manifolds. Embedded contact homology has now been proven to be isomorphic to both monopole Floer homology (Kutluhan–Lee–Taubes) and Heegaard Floer homology (Colin–Ghiggini–Honda). Hutchings has also introduced a sequence of symplectic capacities known as ECH capacities, which have applications to embedding problems for Liouville domains.