Floer homology and square pegs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911954532040704 |
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| author | Greene, Joshua Evan Lobb, Andrew |
| author_facet | Greene, Joshua Evan Lobb, Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Floer homology and square pegs Greene, Joshua Evan Lobb, Andrew Symplectic Geometry Combinatorics Geometric Topology Metric Geometry 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. |
| title | Floer homology and square pegs |
| topic | Symplectic Geometry Combinatorics Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2404.05179 |