3-manifold decision problems and Riemann hypotheses

Abstract

Beginning with Kuperberg's work on unknot recognition, several fundamental decision problems in 3-manifold topology have been shown to be in coNP assuming the generalized Riemann hypothesis. In this note, we explain how recent developments around the quasi-Riemann hypothesis yield unconditional versions of these results, leading for example to the first unconditional proof that 3-sphere recognition is in coNP.