Year: 2026
Type: preprint
Abstract: We resolve an open problem posed by Tao related to the Toeplitz square peg conjecture. We prove that four simple closed polygonal curves in the cylinder, each winding once in the positive direction, jointly inscribe a square whenever the alternating sum of their $\int y\, dx$ integrals vanishes. The proof reduces the problem to the non-displaceability of a pair of Lagrangian tori, which we establish using Lagrangian Floer homology.
Source: arXiv (Cornell University)
Author: Valerio, Lorenzo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222609692