{"status":"public","date_created":"2018-12-11T11:56:02Z","abstract":[{"text":"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.","lang":"eng"}],"publication":"Proceedings of the Annual Symposium on Computational Geometry","date_updated":"2023-09-11T13:38:49Z","quality_controlled":"1","date_published":"2014-06-01T00:00:00Z","year":"2014","day":"01","author":[{"last_name":"Matoušek","full_name":"Matoušek, Jiří","first_name":"Jiří"},{"last_name":"Sedgwick","full_name":"Sedgwick, Eric","first_name":"Eric"},{"full_name":"Tancer, Martin","orcid":"0000-0002-1191-6714","first_name":"Martin","last_name":"Tancer","id":"38AC689C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-1494-0568","first_name":"Uli","full_name":"Wagner, Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"4849","acknowledgement":"ERC Advanced Grant No. 267165; Grant GRADR Eurogiga GIG/11/E023  (SNSF-PP00P2-138948); Swiss National Science Foundation  (SNSF-200020-138230).","language":[{"iso":"eng"}],"department":[{"_id":"UlWa"}],"page":"78 - 84","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1402.0815"}],"related_material":{"record":[{"status":"public","id":"425","relation":"later_version"}]},"publisher":"ACM","oa":1,"scopus_import":1,"conference":{"start_date":"2014-06-08","location":"Kyoto, Japan","end_date":"2014-06-11","name":"SoCG: Symposium on Computational Geometry"},"publication_status":"published","title":"Embeddability in the 3 sphere is decidable","month":"06","_id":"2157","doi":"10.1145/2582112.2582137","type":"conference","citation":{"apa":"Matoušek, J., Sedgwick, E., Tancer, M., &#38; 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>","short":"J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 78–84.","mla":"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>.","chicago":"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>.","ieee":"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.","ista":"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.","ama":"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>"},"oa_version":"Submitted Version"}