On the links of vertices in eimplicial d-complexes embeddable in the euclidean 2d-space

Parsa, S ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1007/s00454-017-9936-1
  3. Publisher: Springer New York LLC , 2018
  4. Abstract:
  5. We consider d-dimensional simplicial complexes which can be PL embedded in the 2d-dimensional Euclidean space. In short, we show that in any such complex, for any three vertices, the intersection of the link-complexes of the vertices is linklessly embeddable in the (2 d- 1 ) -dimensional Euclidean space. In addition, we use similar considerations on links of vertices to derive a new asymptotic upper bound on the total number of d-simplices in an (continuously) embeddable complex in 2d-space with n vertices, improving known upper bounds, for all d≥ 2. Moreover, we show that the same asymptotic bound also applies to the size of d-complexes linklessly embeddable in the (2 d+ 1 ) -dimensional space. © 2017, Springer Science+Business Media, LLC
  6. Keywords:
  7. Embeddability ; F-vector ; Linkless embedding ; Simplicial complex
  8. Source: Discrete and Computational Geometry ; Volume 59, Issue 3 , 2018 , Pages 663-679 ; 01795376 (ISSN)
  9. URL: https://link.springer.com/article/10.1007%2Fs00454-017-9936-1