A Solution to the Periodic Square Peg Problem

TL;DR

This paper proves the periodic square peg problem by applying Lagrangian Floer homology, interpreting inscribed squares as intersections of non-displaceable Lagrangian sub-manifolds in a symplectic 4-torus, providing a novel mathematical approach.

Contribution

It introduces a new Floer homology method to solve the periodic square peg problem, linking symplectic topology with classical geometric problems.

Findings

Inscribed squares correspond to intersections of Lagrangian sub-manifolds.

The problem is resolved using Floer homology techniques.

The approach offers a new perspective on geometric inscribed shape problems.

Abstract

We resolve the periodic square peg problem using a simple Lagrangian Floer homology argument. Inscribed squares are interpreted as intersections between two non-displaceable Lagrangian sub-manifolds of a symplectic 4-torus.