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arXiv · 2309.15504

Embedding simply connected 2-complexes in 3-space

Johannes Carmesin
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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 Lovász, Pardon and U. Wagner. The excluded minors are the cones over $K_5$ and $K_{3,3}$, five related constructions, and the remaining two are obtained from triangulations of the Möbius strip by attaching a disc at its central cycle. Secondly, we extend the above theorem to all simply connected 2-dimensional simplicial complexes.

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Johannes Carmesin. 2023-09-27. Embedding simply connected 2-complexes in 3-space. https://arxiv.org/abs/2309.15504

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