On Codimension One Embedding of Simplicial Complexes

  • Anders BjörnerEmail author
  • Afshin Goodarzi


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.



We thank the referees for very useful remarks. Also, we thank Uli Wagner for valuable comments and for bringing Grünbaum’s paper  [8] to our attention.

This research was supported by the grant VR-2015-05308 from Vetenskapsrådet. Part of the research of the second author has been made possible by the grant KAW-stipendiet 2015.0360 from the Knut and Alice Wallenberg’s Fondation.


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Authors and Affiliations

  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholmSweden
  2. 2.Department of Mathematics, Discrete Geometry GroupFree University of BerlinBerlinGermany

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