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- W4327485094 abstract "We provide a simple characterization of simplicial complexes on few vertices that embed into the $d$-sphere. Namely, a simplicial complex on $d+3$ vertices embeds into the $d$-sphere if and only if its non-faces do not form an intersecting family. As immediate consequences, we recover the classical van Kampen--Flores theorem and provide a topological extension of the ErdH os--Ko--Rado theorem. By analogy with F'ary's theorem for planar graphs, we show in addition that such complexes satisfy the rigidity property that continuous and linear embeddability are equivalent." @default.
- W4327485094 created "2023-03-16" @default.
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- W4327485094 date "2021-09-10" @default.
- W4327485094 modified "2023-09-26" @default.
- W4327485094 title "Embedding dimensions of simplicial complexes on few vertices" @default.
- W4327485094 doi "https://doi.org/10.48550/arxiv.2109.04855" @default.
- W4327485094 hasPublicationYear "2021" @default.
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