Work

The shape invariant of four-dimensional ellipsoids

Year: 2026

Type: article

Abstract: The shape invariant of a symplectic manifold encodes the possible area classes of embedded Lagrangian tori. Potentially this is a powerful invariant, but for most manifolds the shape is unknown. We compute the shape for 4 dimensional symplectic ellipsoids where the ratio of the factors is an integer. The full shape invariant gives stronger embedding obstructions than results obtained by considering only monotone tori.

Source: Mathematische Annalen

DOI: 10.1007/s00208-026-03321-y

Authors: Richard Hind, Jun Zhang

Institutions: University of Notre Dame, University of Science and Technology of China

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Simons Foundation, University of Notre Dame, National Natural Science Foundation of China, University of Science and Technology of China