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.
Citation
Benjamin Burton. Éric Colin de Verdière. Arnaud de Mesmay. "On the complexity of immersed normal surfaces." Geom. Topol. 20 (2) 1061 - 1083, 2016. https://doi.org/10.2140/gt.2016.20.1061
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