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Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-4322 Classical 3-manifold theory — Question 9.4
- Math-4323 Classical 3-manifold theory — Question 9.5
- Math-4324 Hyperbolic geometry — Question 10.1
- Math-4325 Hyperbolic geometry — Question 10.2
- Math-4326 Hyperbolic geometry — Question 10.3
- Math-4327 Hyperbolic geometry — Question 10.4
- Math-4328 Hyperbolic geometry — Question 10.5
- Math-4329 Hyperbolic geometry — Question 10.6
- Math-4330 Hyperbolic geometry — Question 10.8
- Math-4331 Foliated Teichmüller theory — Question 11.1
- Math-4332 Foliated Teichmüller theory — Question 11.2
- Math-4333 Foliated Teichmüller theory — Question 11.4
- Math-4334 Coarse foliations — Question 12.2
- Math-4335 Coarse foliations — Question 12.3
- Math-4336 Numerical invariants — Question 13.1
- Math-4337 Numerical invariants — Question 13.2
- Math-4338 Numerical invariants — Question 13.3
- Math-4339 Numerical invariants — Question 13.4
- Math-4340 Numerical invariants — Question 13.5
- Math-4341 Numerical invariants — Question 13.6
- Math-4342 Numerical invariants — Question 13.7
- Math-4343 Immersed objects — Question 14.2
- Math-4344 Immersed objects — Question 14.3
- Math-4345 Immersed objects — Question 14.5
- Math-4346 Miscellaneous — Question 15.1
- Math-4347 Miscellaneous — Question 15.2
- Math-4348 Problem 1.1 — ([188, Problem 1]) Find a non-trivial knot K with VK (t) = 1.
- Math-4349 Problem 1.2 — ([188, Problem 2]) Characterize those elements of Z[t, t−1] of the form VK(t).
- Math-4350 Problem 1.4 — (J.
- Math-4351 Problem 1.5 — (J.
- Math-4352 Problem 1.6 — (J.
- Math-4353 Problem 1.7 — (J.
- Math-4354 Problem 1.8 — (J.
- Math-4355 Problem 1.9 — (X.-S.
- Math-4356 Problem 1.12 — Categorify other knot polynomials.
- Math-4357 Problem 1.13 — (A.
- Math-4358 Problem 1.15 — (M.
- Math-4359 Problem 1.17 — (A.
- Math-4360 Problem 1.18 — (A.
- Math-4361 Conjecture 1.19 — (The volume conjecture, [198, 296]) For any knot K, 2π·lim N →∞ log|JN (K)| N = v3||S3− K||, (2) where||·||denotes th…
- Math-4362 Problem 1.20 — Justify the above arguments rigorously.
- Math-4363 Conjecture 2.1 — ([220, Problem 1.92 (N)]) Fd(ZK)/Fd+1(ZK) is torsion free for each d.
- Math-4364 Conjecture 2.2 — A(S1; Z) is torsion free.
- Math-4365 Conjecture 2.3 — (X.-S.
- Math-4366 Conjecture 2.5 — Vassiliev invariants distinguish oriented knots.
- Math-4367 Problem 2.6 — Does there exists a non-trivial oriented knot which can not b e distinguished from the trivial knot by Vassiliev inva…
- Math-4368 Conjecture 2.7 — (see [220, Problem 1.89 (B)]) For any oriented knot K, no Vassiliev invariants distinguish K from −K.
- Math-4369 Question 2.8 — (T.
- Math-4370 Problem 2.9 — (X.-S.
- Math-4371 Problem 2.10 — (N.