Short proofs of Tverberg-type theorems for cell complexes

Roman Karasev; Arkadiy Skopenkov

doi:10.1007/s00454-025-00806-6

paper

Short proofs of Tverberg-type theorems for cell complexes

arXiv:2405.05629 · doi:10.1007/s00454-025-00806-6

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 $f : X \to R^{d}$ there are pairwise disjoint faces $I ¨ _{1}, \dots, I ¨ _{r}$ of $X$ such that $f (I ¨ _{1}) \cap \dots f (I ¨ _{r}) \neq = \emptyset$ .

4 pages, the PL and the topological cases are considered separately