{"date_updated":"2025-04-15T06:50:22Z","arxiv":1,"publisher":"ACM","article_number":"5","isi":1,"month":"01","doi":"10.1145/3078632","year":"2018","article_type":"original","oa_version":"Preprint","date_published":"2018-01-01T00:00:00Z","abstract":[{"lang":"eng","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, 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."}],"ec_funded":1,"publication":"Journal of the ACM","_id":"425","external_id":{"arxiv":["1402.0815"],"isi":["000425685900006"]},"author":[{"last_name":"Matoušek","first_name":"Jiří","full_name":"Matoušek, Jiří"},{"full_name":"Sedgwick, Eric","first_name":"Eric","last_name":"Sedgwick"},{"orcid":"0000-0002-1191-6714","last_name":"Tancer","first_name":"Martin","full_name":"Tancer, Martin","id":"38AC689C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Uli","last_name":"Wagner","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"}],"related_material":{"record":[{"id":"2157","relation":"earlier_version","status":"public"}]},"main_file_link":[{"url":"https://arxiv.org/abs/1402.0815","open_access":"1"}],"scopus_import":"1","issue":"1","publist_id":"7398","department":[{"_id":"UlWa"}],"publication_status":"published","volume":65,"oa":1,"date_created":"2018-12-11T11:46:24Z","language":[{"iso":"eng"}],"title":"Embeddability in the 3-Sphere is decidable","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"day":"01","article_processing_charge":"No","status":"public","quality_controlled":"1","type":"journal_article","intvolume":"        65","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Matoušek, Jiří, et al. “Embeddability in the 3-Sphere Is Decidable.” <i>Journal of the ACM</i>, vol. 65, no. 1, 5, ACM, 2018, doi:<a href=\"https://doi.org/10.1145/3078632\">10.1145/3078632</a>.","chicago":"Matoušek, Jiří, Eric Sedgwick, Martin Tancer, and Uli Wagner. “Embeddability in the 3-Sphere Is Decidable.” <i>Journal of the ACM</i>. ACM, 2018. <a href=\"https://doi.org/10.1145/3078632\">https://doi.org/10.1145/3078632</a>.","apa":"Matoušek, J., Sedgwick, E., Tancer, M., &#38; Wagner, U. (2018). Embeddability in the 3-Sphere is decidable. <i>Journal of the ACM</i>. ACM. <a href=\"https://doi.org/10.1145/3078632\">https://doi.org/10.1145/3078632</a>","ista":"Matoušek J, Sedgwick E, Tancer M, Wagner U. 2018. Embeddability in the 3-Sphere is decidable. Journal of the ACM. 65(1), 5.","short":"J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, Journal of the ACM 65 (2018).","ieee":"J. Matoušek, E. Sedgwick, M. Tancer, and U. Wagner, “Embeddability in the 3-Sphere is decidable,” <i>Journal of the ACM</i>, vol. 65, no. 1. ACM, 2018.","ama":"Matoušek J, Sedgwick E, Tancer M, Wagner U. Embeddability in the 3-Sphere is decidable. <i>Journal of the ACM</i>. 2018;65(1). doi:<a href=\"https://doi.org/10.1145/3078632\">10.1145/3078632</a>"}}