Embedding Simply Connected 2-Complexes in 3-Space
Johannes Carmesin · Memoirs of the American Mathematical Society · 2026
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 K_5 and K 3 , 3 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.