Embedding simply connected 2-complexes in 3-space -- V. A refined Kuratowski-type characterisation

2017/09/14 by Johannes Carmesin, Carmesin, Johannes · 1 citation
Computer Science · Mathematics · #05C10 #05C65 #05C83 #32Q40 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Topological and Geometric Data Analysis #math.CO #math.GT #msc:05C10 #msc:05C65 #msc:05C83 #msc:32Q40

paper · pdf · doi:10.48550/arxiv.1709.04659

openalex publication_date 2017/09/14 · arxiv created 2019/09/04 · arxiv updated 2019/09/05 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

This paper is the last paper in a series of five papers. Building on earlier papers in this series, we prove an analogue of Kuratowski's characterisation of graph planarity for three dimensions. More precisely, a simply connected 2-dimensional simplicial complex embeds in 3-space if and only if it has no obstruction from an explicit list of obstructions. This list of obstructions is finite except for one infinite family.

Citations

• Embedding simply connected 2-complexes in 3-space -- III. Constraint minors

Cited by

• Embedding simply connected 2-complexes in 3-space -- II. Rotation systems

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• Embedding simply connected 2-complexes in 3-space -- I. A Kuratowski-type characterisation
• Embedding simply connected 2-complexes in 3-space
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• Embedding simply connected 2-complexes in 3-space -- II. Rotation systems
• Dual matroids of 2-complexes -- revisited