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On codimension one embedding of simplicial complexes

Springer International Publishing, (2017), 207-219
DOI: 10.1007/978-3-319-44479-6_9
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Abstract

We study d-dimensional simplicial complexes that are PL embeddable in Rd+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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Björner, A., & Goodarzi, A. (2017). On codimension one embedding of simplicial complexes. In A Journey through Discrete Mathematics: A Tribute to Jiri Matousek (pp. 207–219). Springer International Publishing. https://doi.org/10.1007/978-3-319-44479-6_9

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