Abstract:We say a d-dimensional simplicial complex embeds into double dimension if it embeds into the Euclidean space of dimension 2d. For instance, a graph is planar iff it embeds into double dimension. We study the conditions under which the join of two simplicial complexes embeds into double dimension. Quite unexpectedly, we show that there exist complexes which do not embed into double dimension, however their join embeds into the respective double dimension. We further derive conditions, in terms of the van Kampen… Show more
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