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On Codimension one Embedding of Simplicial Complexes (1605.01240v2)
Published 4 May 2016 in math.GT and math.CO
Abstract: We study $d$-dimensional simplicial complexes that are PL embeddable in $\mathbb{R}{d+1}$. It is shown that such a complex must satisfy a certain homological condition. The existence of this obstruction allows us to provide a systematic approach to deriving upper bounds for the number of top-dimensional faces of such complexes, particularly in low dimensions.
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