conference paper
Embeddability in the 3 sphere is decidable
published
yes
Jiří
Matoušek
author
Eric
Sedgwick
author
Martin
Tancer
author 38AC689C-F248-11E8-B48F-1D18A9856A870000-0002-1191-6714
Uli
Wagner
author 36690CA2-F248-11E8-B48F-1D18A9856A870000-0002-1494-0568
UlWa
department
SoCG: Symposium on Computational Geometry
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.
ACM2014Kyoto, Japan
eng
Proceedings of the Annual Symposium on Computational Geometry10.1145/2582112.2582137
78 - 84
https://research-explorer.app.ist.ac.at/record/425
Matoušek J, Sedgwick E, Tancer M, Wagner U. 2014. Embeddability in the 3 sphere is decidable. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry 78–84.
Matoušek, Jiří, Eric Sedgwick, Martin Tancer, and Uli Wagner. “Embeddability in the 3 Sphere Is Decidable.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 78–84. ACM, 2014. <a href="https://doi.org/10.1145/2582112.2582137">https://doi.org/10.1145/2582112.2582137</a>.
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>
Matoušek, Jiří, et al. “Embeddability in the 3 Sphere Is Decidable.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 78–84, doi:<a href="https://doi.org/10.1145/2582112.2582137">10.1145/2582112.2582137</a>.
Matoušek, J., Sedgwick, E., Tancer, M., & Wagner, U. (2014). Embeddability in the 3 sphere is decidable. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 78–84). Kyoto, Japan: ACM. <a href="https://doi.org/10.1145/2582112.2582137">https://doi.org/10.1145/2582112.2582137</a>
J. Matoušek, E. Sedgwick, M. Tancer, and U. Wagner, “Embeddability in the 3 sphere is decidable,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 78–84.
J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 78–84.
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