Lagrangian torus invariants using ECH = SWF
arXiv:1910.04553
Abstract
We construct distinguished elements in the embedded contact homology (and monopole Floer homology) of a 3-torus, associated with Lagrangian tori in symplectic 4-manifolds and their isotopy classes. They turn out not to be new invariants, instead they repackage the Gromov (and Seiberg-Witten) invariants of various torus surgeries. We then recover a result of Morgan-Mrowka-Szabó on product formulas for the Seiberg-Witten invariants along 3-tori.
23 pages, to appear in J. Symplectic Geom. with small edits. arXiv admin note: text overlap with arXiv:1905.10938, arXiv:1809.03405