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Embedding dimensions of simplicial complexes on few vertices

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 نشر من قبل Florian Frick
 تاريخ النشر 2021
  مجال البحث
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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 Farys theorem for planar graphs, we show in addition that such complexes satisfy the rigidity property that continuous and linear embeddability are equivalent.



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