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DOI: 10.4230/LIPIcs.SoCG.2016.24
URN: urn:nbn:de:0030-drops-59168
URL: http://drops.dagstuhl.de/opus/volltexte/2016/5916/
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Burton, Benjamin A. ; de Mesmay, Arnaud ; Wagner, Uli

Finding Non-Orientable Surfaces in 3-Manifolds

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LIPIcs-SoCG-2016-24.pdf (0.5 MB)


Abstract

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.

BibTeX - Entry

@InProceedings{burton_et_al:LIPIcs:2016:5916,
  author =	{Benjamin A. Burton and Arnaud de Mesmay and Uli Wagner},
  title =	{{Finding Non-Orientable Surfaces in 3-Manifolds}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{S{\'a}ndor Fekete and Anna Lubiw},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5916},
  URN =		{urn:nbn:de:0030-drops-59168},
  doi =		{10.4230/LIPIcs.SoCG.2016.24},
  annote =	{Keywords: 3-manifold, low-dimensional topology, embedding, non-orientability, normal surfaces}
}

Keywords: 3-manifold, low-dimensional topology, embedding, non-orientability, normal surfaces
Seminar: 32nd International Symposium on Computational Geometry (SoCG 2016)
Issue Date: 2016
Date of publication: 09.06.2016


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