Floer homology and square pegs
Symplectic Geometry
2024-07-16 v2 Combinatorics
Geometric Topology
Metric Geometry
Abstract
We construct a version of Lagrangian Floer homology whose chain complex is generated by the inscriptions of a rectangle into a real analytic Jordan curve. By using its associated spectral invariants, we establish that a rectifiable Jordan curve admits inscriptions of a whole interval of rectangles. In particular, it inscribes a square if the area it encloses is more than half that of a circle of equal diameter.
Cite
@article{arxiv.2404.05179,
title = {Floer homology and square pegs},
author = {Joshua Evan Greene and Andrew Lobb},
journal= {arXiv preprint arXiv:2404.05179},
year = {2024}
}
Comments
29 pages, 9 figures; version 2: updated introduction, streamlined proof of properties of spectral invariants