Floer-type bipersistence modules and rectangle barcodes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916294761119744 |
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| author | Koeda, Kanta Orita, Ryuma Yashiro, Kanon |
| author_facet | Koeda, Kanta Orita, Ryuma Yashiro, Kanon |
| contents | In this paper, we show that the pointwise finite-dimensional two-parameter persistence module $\mathbb{HF}_*^{(\bullet,\bullet]}$, defined in terms of interlevel filtered Floer homology, is rectangle-decomposable. This allows for the definition of a barcode $\mathcal{B}_*^{(\bullet,\bullet]}$ consisting only of rectangles in $\mathbb{R}^2$ associated with $\mathbb{HF}_*^{(\bullet,\bullet]}$. We observe that this rectangle barcode contains information about Usher's boundary depth and spectral invariants developed by Oh, Schwarz, and Viterbo. Moreover, we establish relevant stability results, particularly concerning the bottleneck distance and Hofer's distance. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_07847 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Floer-type bipersistence modules and rectangle barcodes Koeda, Kanta Orita, Ryuma Yashiro, Kanon Symplectic Geometry Algebraic Topology 55N31, 58E05, 57R58, 16G20 In this paper, we show that the pointwise finite-dimensional two-parameter persistence module $\mathbb{HF}_*^{(\bullet,\bullet]}$, defined in terms of interlevel filtered Floer homology, is rectangle-decomposable. This allows for the definition of a barcode $\mathcal{B}_*^{(\bullet,\bullet]}$ consisting only of rectangles in $\mathbb{R}^2$ associated with $\mathbb{HF}_*^{(\bullet,\bullet]}$. We observe that this rectangle barcode contains information about Usher's boundary depth and spectral invariants developed by Oh, Schwarz, and Viterbo. Moreover, we establish relevant stability results, particularly concerning the bottleneck distance and Hofer's distance. |
| title | Floer-type bipersistence modules and rectangle barcodes |
| topic | Symplectic Geometry Algebraic Topology 55N31, 58E05, 57R58, 16G20 |
| url | https://arxiv.org/abs/2312.07847 |