Lagrangian torus invariants using \(ECH=SWF\) (Q2063699)

Embedded contact homology (ECH) is a kind of Floer homology for contact three-manifolds. Taubes has shown that ECH is isomorphic to a version of Seiberg-Witten Floer homology, cf. [\textit{C. H. Taubes}, Geom. Topol. 14, No. 5, 2497--2581 (2010; Zbl 1275.57037)]. The author of the paper under review describes distinguished elements in ECH of a 3-torus, associated with Lagrangian tori in symplectic 4-manifolds and their isotopy classes. These invariants are not new, ``they repackage the Gromov (and Seiberg-Witten) invariants of various torus surgeries''. Finally, the autor ``recovers a result of Morgan-Mrowka-Szabo on product formulas for the Seiberg-Witten invariants along 3-tori [\textit{J. W. Morgan} et al., Math. Res. Lett. 4, No. 6, 915--929 (1997; Zbl 0892.57021)].''