@inproceedings{2157,
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, i.e., an essential curve in the boundary of X bounding a disk in S3 nX 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},
booktitle = {Proceedings of the Annual Symposium on Computational Geometry},
location = {Kyoto, Japan},
pages = {78 -- 84},
publisher = {ACM},
title = {{Embeddability in the 3 sphere is decidable}},
doi = {10.1145/2582112.2582137},
year = {2014},
}