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arXiv · 2405.05629

Short proofs of Tverberg-type theorems for cell complexes

Roman Karasev·Arkadiy Skopenkov
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Abstract

We present short proofs of Tverberg-type theorems for cell complexes by S. Hasui, D. Kishimoto, M. Takeda, and M. Tsutaya. One of them states that for any prime power $r$, any complex $X$ topologically homeomorphic to $S^{(d+1)(r-1)-1}$, and any continuous map $f:X\to\mathbb R^d$ there are pairwise disjoint faces $\sigma_1,\ldots,\sigma_r$ of $X$ such that $f(\sigma_1)\cap\ldots f(\sigma_r)\ne\emptyset$.

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Roman Karasev, Arkadiy Skopenkov. 2024-05-09. Short proofs of Tverberg-type theorems for cell complexes. https://doi.org/10.1007/s00454-025-00806-6

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