Tverberg's theorem for cell complexes

Sho Hasui; Daisuke Kishimoto; Masahiro Takeda; Mitsunobu Tsutaya

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arXiv · 2101.10596

Tverberg's theorem for cell complexes

Sho Hasui·Daisuke Kishimoto·Masahiro Takeda·Mitsunobu Tsutaya

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Abstract

The topological Tverberg theorem states that any continuous map of a $(d+1)(r-1)$-simplex into the Euclidean $d$-space maps some points from $r$ pairwise disjoint faces of the simplex to the same point whenever $r$ is a prime power. We substantially generalize this theorem to continuous maps of certain CW complexes, including simplicial $((d+1)(r-1)-1)$-spheres, into the Euclidean $d$-space. We also discuss the atomicity of the Tverberg property.

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Sho Hasui, Daisuke Kishimoto, Masahiro Takeda, Mitsunobu Tsutaya. 2021-01-26. Tverberg's theorem for cell complexes. https://arxiv.org/abs/2101.10596

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