--- _id: '534' 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. article_processing_charge: No article_type: original author: - first_name: Benjamin full_name: Burton, Benjamin last_name: Burton - first_name: Arnaud N full_name: De Mesmay, Arnaud N id: 3DB2F25C-F248-11E8-B48F-1D18A9856A87 last_name: De Mesmay - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Burton B, de Mesmay AN, Wagner U. Finding non-orientable surfaces in 3-Manifolds. Discrete & Computational Geometry. 2017;58(4):871-888. doi:10.1007/s00454-017-9900-0 apa: Burton, B., de Mesmay, A. N., & Wagner, U. (2017). Finding non-orientable surfaces in 3-Manifolds. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-017-9900-0 chicago: Burton, Benjamin, Arnaud N de Mesmay, and Uli Wagner. “Finding Non-Orientable Surfaces in 3-Manifolds.” Discrete & Computational Geometry. Springer, 2017. https://doi.org/10.1007/s00454-017-9900-0. ieee: B. Burton, A. N. de Mesmay, and U. Wagner, “Finding non-orientable surfaces in 3-Manifolds,” Discrete & Computational Geometry, vol. 58, no. 4. Springer, pp. 871–888, 2017. ista: Burton B, de Mesmay AN, Wagner U. 2017. Finding non-orientable surfaces in 3-Manifolds. Discrete & Computational Geometry. 58(4), 871–888. mla: Burton, Benjamin, et al. “Finding Non-Orientable Surfaces in 3-Manifolds.” Discrete & Computational Geometry, vol. 58, no. 4, Springer, 2017, pp. 871–88, doi:10.1007/s00454-017-9900-0. short: B. Burton, A.N. de Mesmay, U. Wagner, Discrete & Computational Geometry 58 (2017) 871–888. date_created: 2018-12-11T11:47:01Z date_published: 2017-06-09T00:00:00Z date_updated: 2023-02-21T17:01:34Z day: '09' department: - _id: UlWa doi: 10.1007/s00454-017-9900-0 external_id: arxiv: - '1602.07907' intvolume: ' 58' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1602.07907 month: '06' oa: 1 oa_version: Preprint page: 871 - 888 publication: Discrete & Computational Geometry publication_identifier: issn: - '01795376' publication_status: published publisher: Springer publist_id: '7283' quality_controlled: '1' related_material: record: - id: '1379' relation: earlier_version status: public scopus_import: 1 status: public title: Finding non-orientable surfaces in 3-Manifolds type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 58 year: '2017' ...