@article{425,
abstract = {We show that the following algorithmic problem is decidable: given a 2-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in R3? By a known reduction, it suffices to decide the embeddability of a given triangulated 3-manifold X into the 3-sphere S3. The main step, which allows us to simplify X and recurse, is in proving that if X can be embedded in S3, then there is also an embedding in which X has a short meridian, that is, an essential curve in the boundary of X bounding a disk in S3 \ X with length bounded by a computable function of the number of tetrahedra of X.},
author = {Matoušek, Jiří and Sedgwick, Eric and Tancer, Martin and Wagner, Uli},
journal = {Journal of the ACM},
number = {1},
publisher = {ACM},
title = {{Embeddability in the 3-Sphere is decidable}},
doi = {10.1145/3078632},
volume = {65},
year = {2018},
}