On the Complexity of Immersed Normal Surfaces
Geometric Topology
2016-05-04 v1 Computational Geometry
Abstract
Normal surface theory, a tool to represent surfaces in a triangulated 3-manifold combinatorially, is ubiquitous in computational 3-manifold theory. In this paper, we investigate a relaxed notion of normal surfaces where we remove the quadrilateral conditions. This yields normal surfaces that are no longer embedded. We prove that it is NP-hard to decide whether such a surface is immersed. Our proof uses a reduction from Boolean constraint satisfaction problems where every variable appears in at most two clauses, using a classification theorem of Feder. We also investigate variants, and provide a polynomial-time algorithm to test for a local version of this problem.
Cite
@article{arxiv.1412.4988,
title = {On the Complexity of Immersed Normal Surfaces},
author = {Benjamin A. Burton and Éric Colin de Verdière and Arnaud de Mesmay},
journal= {arXiv preprint arXiv:1412.4988},
year = {2016}
}
Comments
17 pages, under journal submission