Hardness of almost embedding simplicial complexes in $$\mathbb {R}^d$$ R d
نویسندگان
چکیده
منابع مشابه
Hardness of almost embedding simplicial complexes in $\mathbb R^d$
A map f : K → R of a simplicial complex is an almost embedding if f(σ) ∩ f(τ) = ∅ whenever σ, τ are disjoint simplices of K. Theorem. Fix integers d, k ≥ 2 such that d = 3k 2 + 1. (a) Assume that P 6= NP . Then there exists a finite k-dimensional complex K that does not admit an almost embedding in R but for which there exists an equivariant map K̃ → Sd−1. (b) The algorithmic problem of recognit...
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Let EMBEDk→d be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k, does there exist a (piecewise linear) embedding ofK into R? Known results easily imply polynomiality of EMBEDk→2 (k = 1, 2; the case k = 1, d = 2 is graph planarity) and of EMBEDk→2k for all k ≥ 3 (even if k is not considered fixed). We show that the celebrated result of Novikov on the...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2018
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-018-0013-1