Embedding simply connected 2-complexes in 3-space
Combinatorics
2023-09-28 v1 Geometric Topology
Abstract
Firstly, 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 nine excluded minors. This answers questions of Lov\'asz, Pardon and U. Wagner. The excluded minors are the cones over and , five related constructions, and the remaining two are obtained from triangulations of the M\"obius strip by attaching a disc at its central cycle. Secondly, we extend the above theorem to all simply connected 2-dimensional simplicial complexes.
Cite
@article{arxiv.2309.15504,
title = {Embedding simply connected 2-complexes in 3-space},
author = {Johannes Carmesin},
journal= {arXiv preprint arXiv:2309.15504},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1709.04643