Finding non-orientable surfaces in 3-manifolds
Geometric Topology
2016-09-02 v2 Computational Geometry
Abstract
We investigate the complexity of finding an embedded non-orientable surface of Euler genus in a triangulated -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 -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.
Cite
@article{arxiv.1602.07907,
title = {Finding non-orientable surfaces in 3-manifolds},
author = {Benjamin A. Burton and Arnaud de Mesmay and Uli Wagner},
journal= {arXiv preprint arXiv:1602.07907},
year = {2016}
}
Comments
v2: minor changes