Embedding simply connected 2-complexes in 3-space

2023/09/27 by Carmesin, Johannes
#05C10 #05C65 #05C83 #32Q40 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2309.15504

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 K₅ 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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