The complexity of detecting taut angle structures on triangulations

Benjamin A. Burton; Jonathan Spreer

doi:10.1137/1.9781611973105.13

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arXiv · 1207.0904

The complexity of detecting taut angle structures on triangulations

Benjamin A. Burton·Jonathan Spreer

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Abstract

There are many fundamental algorithmic problems on triangulated 3-manifolds whose complexities are unknown. Here we study the problem of finding a taut angle structure on a 3-manifold triangulation, whose existence has implications for both the geometry and combinatorics of the triangulation. We prove that detecting taut angle structures is NP-complete, but also fixed-parameter tractable in the treewidth of the face pairing graph of the triangulation. These results have deeper implications: the core techniques can serve as a launching point for approaching decision problems such as unknot recognition and prime decomposition of 3-manifolds.

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Benjamin A. Burton, Jonathan Spreer. 2012-07-04. The complexity of detecting taut angle structures on triangulations. https://doi.org/10.1137/1.9781611973105.13

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