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Bibliographic Details
Main Authors: Nakajima, Yuto, Watanabe, Takayuki
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.06004
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Table of 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.