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arXiv · 2404.05179

Floer homology and square pegs

Joshua Evan Greene·Andrew Lobb
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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.

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Joshua Evan Greene, Andrew Lobb. 2024-04-08. Floer homology and square pegs. https://arxiv.org/abs/2404.05179

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