On Codimension one Embedding of Simplicial Complexes

Anders Björner; Afshin Goodarzi

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arXiv · 1605.01240

On Codimension one Embedding of Simplicial Complexes

Anders Björner·Afshin Goodarzi

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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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Anders Björner, Afshin Goodarzi. 2016-05-04. On Codimension one Embedding of Simplicial Complexes. https://arxiv.org/abs/1605.01240

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