Embedding simply connected 2-complexes in 3-space -- IV. Dual matroids
Combinatorics
2017-09-15 v1 Geometric Topology
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.
Cite
@article{arxiv.1709.04652,
title = {Embedding simply connected 2-complexes in 3-space -- IV. Dual matroids},
author = {Johannes Carmesin},
journal= {arXiv preprint arXiv:1709.04652},
year = {2017}
}