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Article Dans Une Revue Discrete and Computational Geometry Année : 2017

Finding Non-orientable Surfaces in 3-Manifolds

Résumé

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.

Dates et versions

hal-01539682 , version 1 (15-06-2017)

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Benjamin A. Burton, Arnaud de Mesmay, Uli Wagner. Finding Non-orientable Surfaces in 3-Manifolds. Discrete and Computational Geometry, 2017, 58 (4), pp.871--888. ⟨10.1007/s00454-017-9900-0⟩. ⟨hal-01539682⟩
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