Finding Non-Orientable Surfaces in 3-Manifolds

@article{Burton2016FindingNS,
  title={Finding Non-Orientable Surfaces in 3-Manifolds},
  author={Benjamin A. Burton and A. D. Mesmay and Uli Wagner},
  journal={ArXiv},
  year={2016},
  volume={abs/1602.07907}
}
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… Expand
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