On approximability by embeddings of cycles in the plane.

DOI10.1016/S0166-8641(03)00069-5zbMath1039.57015arXiv0808.1187MaRDI QIDQ1409758

Mikhail Skopenkov

Publication date: 22 October 2003

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.1187

zbMATH Keywords

approximability by embeddingsderivative of a graphderivative of a simplicial mapstandard d-windingtransversal self-intersectionVan Kampen obstruction

Mathematics Subject Classification ID

Related Items (15)

Bad drawings of small complete graphs ⋮ Atomic Embeddability, Clustered Planarity, and Thickenability ⋮ Recognizing weakly simple polygons ⋮ \(c\)-planarity of embedded cyclic \(c\)-graphs ⋮ Hanani-Tutte for radial planarity. II ⋮ Hanani-Tutte for Radial Planarity II ⋮ Embedding graphs into embedded graphs ⋮ Hardness of almost embedding simplicial complexes in \(\mathbb {R}^d\) ⋮ Crossing minimization in perturbed drawings ⋮ Stability of intersections of graphs in the plane and the van Kampen obstruction ⋮ Crossing minimization in perturbed drawings ⋮ Unnamed Item ⋮ Hanani-Tutte for approximating maps of graphs ⋮ The van Kampen obstruction and its relatives ⋮ Embedding Graphs into Embedded Graphs

Cites Work

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• Obstructions to approximating maps of \(n\)-manifolds into \(\mathbb{R}^{2n}\) by embeddings
• A one-dimensional Whitney trick and Kuratowski's graph planarity criterion
• Moving compacta in \(\mathbb{R}{}^ m\) apart
• A deleted product criterion for approximability of maps by embeddings
• Open problems on graphs arising from geometric topology
• On simplicial maps and chainable continua
• Van Kampen's embedding obstruction is incomplete for 2-complexes in \(\mathbb{R}^ 4\)
• Moduli of Riemann surfaces, Hurwitz-type spaces, and their superanalogues
• Realization of mappings
• Komplexe in euklidischen Räumen

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