Embeddability in the 3 sphere is decidable
Matoušek, Jiří
Sedgwick, Eric
Tancer, Martin
Wagner, Uli
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.
ACM
2014
info:eu-repo/semantics/conferenceObject
doc-type:conferenceObject
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http://purl.org/coar/resource_type/c_5794
https://research-explorer.app.ist.ac.at/record/2157
Matoušek J, Sedgwick E, Tancer M, Wagner U. Embeddability in the 3 sphere is decidable. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:78-84. doi:<a href="https://doi.org/10.1145/2582112.2582137">10.1145/2582112.2582137</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1145/2582112.2582137
info:eu-repo/semantics/openAccess