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

Parsa, S ; Sharif University of Technology

121 Viewed
  1. Type of Document: Article
  2. DOI: 10.1007/s00454-017-9936-1
  3. Abstract:
  4. 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 (Formula presented.)-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 (Formula presented.). Moreover, we show that the same asymptotic bound also applies to the size of d-complexes linklessly embeddable in the (Formula presented.)-dimensional space. © 2017 Springer Science+Business Media, LLC
  5. Keywords:
  6. Embeddability ; F-vector ; Linkless embedding ; Simplicial complex
  7. Source: Discrete and Computational Geometry ; 2017 , Pages 1-17 ; 01795376 (ISSN)
  8. URL: https://link.springer.com/article/10.1007/s00454-017-9936-1