Floer homology and square pegs

Floer homology and square pegs

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....

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Veröffentlicht in:arXiv.org 2024-07
Hauptverfasser: Greene, Joshua Evan, Lobb, Andrew
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Homology
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description 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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Rectangles
title Floer homology and square pegs
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