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

2017/09/14 by Johannes Carmesin, Carmesin, Johannes · 1 citation
Mathematics · #05C10 #05C65 #05C83 #32Q40 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #math.CO #math.GT #msc:05C10 #msc:05C65 #msc:05C83 #msc:32Q40

paper · pdf · doi:10.48550/arxiv.1709.04642

arxiv created 2019/09/04 · arxiv updated 2019/09/05

Abstract

We characterise the embeddability of simply connected locally 3-connected 2-dimensional simplicial complexes in 3-space in a way analogous to Kuratowski's characterisation of graph planarity, by excluded minors. This answers questions of Lovász, Pardon and Wagner.

Cited by

• Minor-excluded graphs and soficity

Related

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