Original sentence: Expanding both on this and on the equivalence of the Seiberg-Witten and Gromov invariants, Taubes has also proven (in a long series of preprints, beginning with ) that a contact 3-manifold's Embedded Contact Homology is isomorphic to a version of its Seiberg--Witten Floer cohomology.More recently, in , by using Seiberg--Witten Floer homology as developed by Peter Kronheimer and Tomasz Mrowka  together with some new estimates on the spectral flow of Dirac operators and some methods from ), Taubes proved the longstanding Weinstein conjecture for all three-dimensional contact manifolds, thus establishing that the Reeb vector field on such a manifold always has a closed orbit
Edited sentence: Expanding both on this and on the equivalence of the Seiberg-Witten and Gromov invariants, Taubes has also proven (in a long series of preprints, beginning with ) that a contact 3-manifold's Embedded Contact Homology is isomorphic to a version of its Seiberg—Witten Floer cohomology.More recently, in , by using Seiberg—Witten Floer homology as developed by Peter Kronheimer and Tomasz Mrowka  together with some new estimates on the spectral flow of Dirac operators and some methods from ), Taubes proved the longstanding Weinstein conjecture for all three-dimensional contact manifolds, thus establishing that the Reeb vector field on such a manifold always has a closed orbit