TL;DR
This paper constructs invariants related to Lagrangian tori in symplectic 4-manifolds using embedded contact homology, linking them to Gromov and Seiberg-Witten invariants and deriving product formulas for these invariants.
Contribution
It introduces a method to reinterpret Gromov and Seiberg-Witten invariants via embedded contact homology for 3-tori, providing new insights into their structure.
Findings
Repackaging of Gromov and Seiberg-Witten invariants for torus surgeries
Recovery of Morgan-Mrowka-Szabó product formulas for Seiberg-Witten invariants
Construction of distinguished elements in ECH related to Lagrangian tori
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-Szab\'o on product formulas for the Seiberg-Witten invariants along 3-tori.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.