{"department":[{"_id":"UlWa"}],"article_processing_charge":"No","external_id":{"arxiv":["1602.07907"]},"article_type":"original","doi":"10.1007/s00454-017-9900-0","title":"Finding non-orientable surfaces in 3-Manifolds","publication_identifier":{"issn":["01795376"]},"oa":1,"abstract":[{"lang":"eng","text":"We investigate the complexity of finding an embedded non-orientable surface of Euler genus g in a triangulated 3-manifold. This problem occurs both as a natural question in low-dimensional topology, and as a first non-trivial instance of embeddability of complexes into 3-manifolds. We prove that the problem is NP-hard, thus adding to the relatively few hardness results that are currently known in 3-manifold topology. In addition, we show that the problem lies in NP when the Euler genus g is odd, and we give an explicit algorithm in this case."}],"date_created":"2018-12-11T11:47:01Z","author":[{"first_name":"Benjamin","last_name":"Burton","full_name":"Burton, Benjamin"},{"first_name":"Arnaud N","id":"3DB2F25C-F248-11E8-B48F-1D18A9856A87","full_name":"De Mesmay, Arnaud N","last_name":"De Mesmay"},{"orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","last_name":"Wagner","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"intvolume":"        58","publisher":"Springer","year":"2017","volume":58,"date_published":"2017-06-09T00:00:00Z","citation":{"apa":"Burton, B., de Mesmay, A. N., &#38; Wagner, U. (2017). Finding non-orientable surfaces in 3-Manifolds. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-017-9900-0\">https://doi.org/10.1007/s00454-017-9900-0</a>","ista":"Burton B, de Mesmay AN, Wagner U. 2017. Finding non-orientable surfaces in 3-Manifolds. Discrete &#38; Computational Geometry. 58(4), 871–888.","ama":"Burton B, de Mesmay AN, Wagner U. Finding non-orientable surfaces in 3-Manifolds. <i>Discrete &#38; Computational Geometry</i>. 2017;58(4):871-888. doi:<a href=\"https://doi.org/10.1007/s00454-017-9900-0\">10.1007/s00454-017-9900-0</a>","chicago":"Burton, Benjamin, Arnaud N de Mesmay, and Uli Wagner. “Finding Non-Orientable Surfaces in 3-Manifolds.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2017. <a href=\"https://doi.org/10.1007/s00454-017-9900-0\">https://doi.org/10.1007/s00454-017-9900-0</a>.","ieee":"B. Burton, A. N. de Mesmay, and U. Wagner, “Finding non-orientable surfaces in 3-Manifolds,” <i>Discrete &#38; Computational Geometry</i>, vol. 58, no. 4. Springer, pp. 871–888, 2017.","mla":"Burton, Benjamin, et al. “Finding Non-Orientable Surfaces in 3-Manifolds.” <i>Discrete &#38; Computational Geometry</i>, vol. 58, no. 4, Springer, 2017, pp. 871–88, doi:<a href=\"https://doi.org/10.1007/s00454-017-9900-0\">10.1007/s00454-017-9900-0</a>.","short":"B. Burton, A.N. de Mesmay, U. Wagner, Discrete &#38; Computational Geometry 58 (2017) 871–888."},"type":"journal_article","publication":"Discrete & Computational Geometry","related_material":{"record":[{"relation":"earlier_version","id":"1379","status":"public"}]},"oa_version":"Preprint","status":"public","issue":"4","scopus_import":1,"language":[{"iso":"eng"}],"page":"871 - 888","_id":"534","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","day":"09","month":"06","main_file_link":[{"url":"https://arxiv.org/abs/1602.07907","open_access":"1"}],"publist_id":"7283","publication_status":"published","date_updated":"2023-02-21T17:01:34Z"}