2024/04/08 by Greene, Joshua Evan, Lobb, Andrew
#Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2404.05179
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.