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

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.

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• Integer homology 3-spheres admit irreducible representations in SL(2,C)
• Embedding simply connected 2-complexes in 3-space -- II. Rotation systems
• Embedding simply connected 2-complexes in 3-space -- IV. Dual matroids
• Embedding simply connected 2-complexes in 3-space -- III. Constraint minors
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Cited by in corpus (3)

• Embedding simply connected 2-complexes in 3-space -- II. Rotation systems
• Multibranched surfaces in 3-manifolds
• Geometric Embeddability of Complexes is $\exists \mathbb{R}$-complete