$2$-complexes with unique embeddings in 3-space
Combinatorics
2021-09-10 v1 Geometric Topology
Abstract
A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected -complex every link graph of which is 3-connected admits an essentially unique locally flat embedding into the 3-sphere, if it admits one at all. This can be thought of as a generalisation of the 3-dimensional Schoenflies theorem.
Cite
@article{arxiv.2109.04085,
title = {$2$-complexes with unique embeddings in 3-space},
author = {Agelos Georgakopoulos and Jaehoon Kim},
journal= {arXiv preprint arXiv:2109.04085},
year = {2021}
}