Title:
Embedding Dimensions of Simplicial Complexes on Few Vertices
Author(s):
Frick, Florian; Hu, Mirabel; Scheel, Verity; Simon, Steven
Year of publication:
2023
Available Date:
2023-10-24T07:41:44Z
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 Erdős–Ko–Rado theorem. By analogy with Fáry’s theorem for planar graphs, we show in addition that such complexes satisfy the rigidity property that continuous and linear embeddability are equivalent.
Part of Identifier:
e-ISSN (online): 0219-3094
Keywords:
simplicial complexes
simple characterization
few vertices
DDC-Classification:
510 Mathematik
Publication Type:
Wissenschaftlicher Artikel
URL of the Original Publication:
DOI of the Original Publication:
Journaltitle:
Annals of Combinatorics
Department/institution:
Mathematik und Informatik
Institut für Mathematik