Year: 2026
Type: article
Abstract: We study exotic Lagrangian tori in dimension four. In certain Stein domains B d p q (which naturally appear in almost toric fibrations) we find d + 1 families of monotone Lagrangian tori which are mutually distinct, up to symplectomorphisms. We prove that these remain distinct under embeddings of B d p q into geometrically bounded symplectic four-manifolds. We show that there are infinitely many different such embeddings when X is compact and (almost) toric and hence conclude that X contains arbitrarily many Lagrangian tori which are distinct up to symplectomorphisms of X . In dimension four arbitrarily many different Lagrangian tori were previously known only in del Pezzo surfaces. Neither the embedded tori, nor the ambient space X needs to be monotone for our methods to work.
Source: Annales de l’institut Fourier
DOI: 10.5802/aif.3789
Authors: Joé Brendel, Johannes Hauber, Joel Schmitz
Institutions: ETH Zurich, University of Neuchâtel
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4392427201