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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.06004 |
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| _version_ | 1866911492750704640 |
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| author | Nakajima, Yuto Watanabe, Takayuki |
| author_facet | Nakajima, Yuto Watanabe, Takayuki |
| contents | We investigate slices of the Sierpiński tetrahedron from a topological viewpoint. For each $c\in[0,1]$, we study the Čech (co)homology group of the slice at height $c$. We show that the topology of the slice exhibits a sharp dichotomy. If $c$ is a dyadic rational, then the slice has finitely many connected components, infinite first Čech homology, and trivial higher homology. If $c$ is not a dyadic rational, then the slice is totally disconnected and all positive-degree Čech homology groups vanish. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06004 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topology of slices through the Sierpiński tetrahedron Nakajima, Yuto Watanabe, Takayuki Dynamical Systems Algebraic Topology We investigate slices of the Sierpiński tetrahedron from a topological viewpoint. For each $c\in[0,1]$, we study the Čech (co)homology group of the slice at height $c$. We show that the topology of the slice exhibits a sharp dichotomy. If $c$ is a dyadic rational, then the slice has finitely many connected components, infinite first Čech homology, and trivial higher homology. If $c$ is not a dyadic rational, then the slice is totally disconnected and all positive-degree Čech homology groups vanish. |
| title | Topology of slices through the Sierpiński tetrahedron |
| topic | Dynamical Systems Algebraic Topology |
| url | https://arxiv.org/abs/2603.06004 |