TY - JOUR
AB - 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.
AU - Matoušek, Jiří
AU - Sedgwick, Eric
AU - Tancer, Martin
AU - Wagner, Uli
ID - 425
IS - 1
JF - Journal of the ACM
TI - Embeddability in the 3-Sphere is decidable
VL - 65
ER -