{"doi":"10.1145/2582112.2582137","year":"2014","status":"public","quality_controlled":"1","_id":"2157","publisher":"ACM","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","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"}],"page":"78 - 84","department":[{"_id":"UlWa"}],"scopus_import":1,"publist_id":"4849","publication":"Proceedings of the Annual Symposium on Computational Geometry","date_updated":"2020-08-11T10:10:11Z","conference":{"start_date":"2014-06-08","end_date":"2014-06-11","name":"SoCG: Symposium on Computational Geometry","location":"Kyoto, Japan"},"acknowledgement":"ERC Advanced Grant No. 267165; Grant GRADR Eurogiga GIG/11/E023 (SNSF-PP00P2-138948); Swiss National Science Foundation (SNSF-200020-138230).","related_material":{"record":[{"relation":"later_version","id":"425","status":"public"}]},"oa":1,"author":[{"first_name":"Jiří","full_name":"Matoušek, Jiří","last_name":"Matoušek"},{"first_name":"Eric","full_name":"Sedgwick, Eric","last_name":"Sedgwick"},{"last_name":"Tancer","orcid":"0000-0002-1191-6714","id":"38AC689C-F248-11E8-B48F-1D18A9856A87","full_name":"Tancer, Martin","first_name":"Martin"},{"orcid":"0000-0002-1494-0568","last_name":"Wagner","first_name":"Uli","full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T11:56:02Z","language":[{"iso":"eng"}],"month":"06","oa_version":"Submitted Version","citation":{"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: *Proceedings of the Annual Symposium on Computational Geometry*. ACM; 2014:78-84. doi:10.1145/2582112.2582137","chicago":"Matoušek, Jiří, Eric Sedgwick, Martin Tancer, and Uli Wagner. “Embeddability in the 3 Sphere Is Decidable.” In *Proceedings of the Annual Symposium on Computational Geometry*, 78–84. ACM, 2014. https://doi.org/10.1145/2582112.2582137.","mla":"Matoušek, Jiří, et al. “Embeddability in the 3 Sphere Is Decidable.” *Proceedings of the Annual Symposium on Computational Geometry*, ACM, 2014, pp. 78–84, doi:10.1145/2582112.2582137.","apa":"Matoušek, J., Sedgwick, E., Tancer, M., & Wagner, U. (2014). Embeddability in the 3 sphere is decidable. In *Proceedings of the Annual Symposium on Computational Geometry* (pp. 78–84). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582137","ieee":"J. Matoušek, E. Sedgwick, M. Tancer, and U. Wagner, “Embeddability in the 3 sphere is decidable,” in *Proceedings of the Annual Symposium on Computational Geometry*, Kyoto, Japan, 2014, pp. 78–84.","short":"J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 78–84."},"title":"Embeddability in the 3 sphere is decidable","date_published":"2014-06-01T00:00:00Z","day":"01","publication_status":"published","type":"conference","main_file_link":[{"url":"http://arxiv.org/abs/1402.0815","open_access":"1"}]}