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DOI: 10.4230/LIPIcs.SoCG.2016.24
URN: urn:nbn:de:0030-drops-59168
URL: https://drops.dagstuhl.de/opus/volltexte/2016/5916/
Burton, Benjamin A. ; de Mesmay, Arnaud ; Wagner, Uli
Finding Non-Orientable Surfaces in 3-Manifolds
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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: | 10.06.2016 |
