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Problems known to be open in the literature and any problem that, after being posed, is decided to be open by the community.

18 votes
Accepted

List of number theoretic or algebraic problems in various complexity classes

Algebraic geometry Noether's Normalization Lemma (NNL) for explicit varieties is currently only known to be in $\mathsf{EXPSPACE}$ (like general NNL), but is conjectured to be in $\mathsf{P}$ (and i …
Joshua Grochow's user avatar
5 votes

Is the 3-sphere recognition problem NP-complete?

This paper shows (though I have not verified it) that 3-sphere recognition* is in coNP assuming GRH: Raphael Zentner. Integer homology 3-spheres admit irreducible representations in $SL(2,\mathbb{C}) …
Joshua Grochow's user avatar