# On the Links of Vertices in Simplicial d-Complexes Embeddable in the Euclidean 2d-Space

@article{Parsa2018OnTL,
title={On the Links of Vertices in Simplicial d-Complexes Embeddable in the Euclidean 2d-Space},
author={Salman Parsa},
journal={Discrete \& Computational Geometry},
year={2018},
volume={59},
pages={663-679}
}
• S. Parsa
• Published 16 December 2015
• Mathematics
• Discrete & Computational Geometry
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 $$(2d-1)$$(2d-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…
11 Citations

### Correction to: On the Links of Vertices in Simplicial d-Complexes Embeddable in the Euclidean 2d-Space

• S. Parsa
• Mathematics
Discret. Comput. Geom.
• 2020
In the following we refer to the original paper [1]. The main reason for writing this correction is the incorrect statement of Theorem 4. Section 4.1 should be corrected by replacing [3] = {1, 2, 3},

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