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On the links of vertices in simplicial d-complexes embeddable in the euclidean 2d-space
, Article Discrete and Computational Geometry ; 2017 , Pages 1-17 ; 01795376 (ISSN) ; Sharif University of Technology
Abstract
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...
On the links of vertices in eimplicial d-complexes embeddable in the euclidean 2d-space
, Article Discrete and Computational Geometry ; Volume 59, Issue 3 , 2018 , Pages 663-679 ; 01795376 (ISSN) ; Sharif University of Technology
Springer New York LLC
2018
Abstract
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...