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Dual matroids of 2-complexes -- revisited

2022/10/27 by Johannes Carmesin, Carmesin, Johannes
Computer Science · #Topological and Geometric Data Analysis #Computational Geometry and Mesh Generation #Constraint Satisfaction and Optimization

paper · pdf · doi:10.48550/arxiv.2210.15594

Abstract

We prove that simply connected local 2-dimensional simplicial complexes embed in 3-space if and only if their dual matroids are graphic. Examples are provided that the assumptions of simply connectedness and locality are necessary. This may be regarded as a 3-dimensional analogue of Whitney's planarity criterion from 1932.

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