Some conditionally hard problems on links and 3-manifolds

Marc Lackenby

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arXiv · 1602.08427

Some conditionally hard problems on links and 3-manifolds

Marc Lackenby

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Abstract

We show that three natural decision problems about links and 3-manifolds are computationally hard, assuming some conjectures in complexity theory. The first problem is determining whether a link in the 3-sphere bounds a Seifert surface with Thurston norm at most a given integer; this is shown to be NP-complete. The second problem is the homeomorphism problem for closed 3-manifolds; this is shown to be at least as hard as the graph isomorphism problem. The third problem is determining whether a given link in the 3-sphere is a sublink of another given link; this is shown to be NP-hard.

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Marc Lackenby. 2016-02-26. Some conditionally hard problems on links and 3-manifolds. https://arxiv.org/abs/1602.08427

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