{"publication_identifier":{"issn":["01795376"]},"publist_id":"7283","article_type":"original","intvolume":"        58","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.07907"}],"language":[{"iso":"eng"}],"year":"2017","day":"09","date_updated":"2023-02-21T17:01:34Z","publication":"Discrete & Computational Geometry","doi":"10.1007/s00454-017-9900-0","oa_version":"Preprint","page":"871 - 888","oa":1,"external_id":{"arxiv":["1602.07907"]},"publisher":"Springer","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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","quality_controlled":"1","volume":58,"_id":"534","status":"public","article_processing_charge":"No","type":"journal_article","issue":"4","department":[{"_id":"UlWa"}],"scopus_import":1,"date_created":"2018-12-11T11:47:01Z","date_published":"2017-06-09T00:00:00Z","title":"Finding non-orientable surfaces in 3-Manifolds","citation":{"short":"B. Burton, A.N. de Mesmay, U. Wagner, Discrete &#38; Computational Geometry 58 (2017) 871–888.","ista":"Burton B, de Mesmay AN, Wagner U. 2017. Finding non-orientable surfaces in 3-Manifolds. Discrete &#38; Computational Geometry. 58(4), 871–888.","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.","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>","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>.","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>.","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>"},"month":"06","author":[{"first_name":"Benjamin","last_name":"Burton","full_name":"Burton, Benjamin"},{"id":"3DB2F25C-F248-11E8-B48F-1D18A9856A87","first_name":"Arnaud N","last_name":"De Mesmay","full_name":"De Mesmay, Arnaud N"},{"full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"id":"1379","status":"public","relation":"earlier_version"}]}}