Embedding simply connected 2-complexes in 3-space -- IV. Dual matroids

2017/09/14 by Johannes Carmesin, Carmesin, Johannes
Computer Science · Mathematics · #05B35 #05C10 #05C65 #05C83 #32Q40 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Data Management and Algorithms #Digital Image Processing Techniques #FOS: Mathematics #Geometric Topology (math.GT) #math.CO #math.GT #msc:05B35 #msc:05C10 #msc:05C65 #msc:05C83 #msc:32Q40

paper · pdf · doi:10.48550/arxiv.1709.04652

arxiv created 2017/09/14 · openalex publication_date 2017/09/14 · arxiv updated 2017/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce dual matroids of 2-dimensional simplicial complexes. Under certain necessary conditions, duals matroids are used to characterise embeddability in 3-space in a way analogous to Whitney's planarity criterion. We further use dual matroids to extend a 3-dimensional analogue of Kuratowski's theorem to the class of 2-dimensional simplicial complexes obtained from simply connected ones by identifying vertices or edges.

Citations

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

Related

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