Mathematics catalogue
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-13201 Conjecture 5.3 — Let hX be as above.
- Math-13202 Problem 5.6 — Compute the quandle cocycle invariant Φ α(K) of each knot K for a second cohomology class α of a connected quandle.
- Math-13203 Problem 5.7 — Find relations between quandle cocycle invariants and knot in- variants known so far, such as quantum invariants.
- Math-13204 Problem 5.8 — Compute H 2 Q(X; A) for each X -module A.
- Math-13205 Problem 5.9 — Let the notation be as above.
- Math-13206 Problem 5.10 — (M.
- Math-13207 Problem 6.3 — (S.J.
- Math-13208 Problem 7.4 — Find a 3-dimensional topological interpretation of quantu m in- variants of 3-manifolds.
- Math-13209 Problem 7.8 — (J.E.
- Math-13210 Problem 7.14 — (D.
- Math-13211 Problem 7.15 — (D.
- Math-13212 Problem 7.17 — (T.
- Math-13213 Problem 7.23 — (S.
- Math-13214 Problem 7.26 — For each rational homology 3-sphere M, calculate τ SO(3)(M ) and τ P SU (N )(M ) for all degrees.
- Math-13215 Problem 7.27 — (J.
- Math-13216 Problem 8.4 — Find other spin TQFT’s.
- Math-13217 Problem 8.5 — Formulate and find spin c TQFT’s.
- Math-13218 Problem 8.7 — (V.
- Math-13219 Problem 8.9 — (G.
- Math-13220 Problem 8.11 — (G.
- Math-13221 Problem 9.7 — (Y.
- Math-13222 Problem 9.8 — (Y.
- Math-13223 Problem 10.2 — (V.
- Math-13224 Question 10.5 — (M.
- Math-13225 Problem 10.11 — Describe Vogel’s algebra Λ, say, by giving complete sets of generators and relations of Λ.
- Math-13226 Problem 10.13 — (J.
- Math-13227 Conjecture 10.14 — The map (50) is an isomorphism.
- Math-13228 Problem 10.16 — (T.
- Math-13229 Problem 10.18 — (F.
- Math-13230 Problem 11.8 — (T.
- Math-13231 Problem 11.10 — (D.
- Math-13232 Question 12.1 — (R.
- Math-13233 Conjecture 12.2 — (R.
- Math-13234 Problem 12.13 — (J.
- Math-13235 Conjecture 12.16 — (X.-S.
- Math-13236 Problem 12.17 — (X.-S.
- Math-13237 Problem 12.18 — (J.
- Math-13238 Problem 12.19 — (J.
- Math-13239 Problem 12.20 — (J.
- Math-13240 Problem 12.22 — (T.
- Math-13241 Virtual-knot problem 3 — The Flat Hierarchy
- Math-13242 Virtual-knot problem 5 — Virtual Three Manifolds
- Math-13243 Virtual-knot problem 18 — Wild Virtuals
- Math-13244 Virtual-knot problem 23 — Find new geometric/topological interpretations for the Jones polynomial and for Khovanov homology.
- Math-13245 Virtual-knot problem 24 — Does it follow that $K$ and $K'$ are equivalent as classical knots?
- Math-13246 Virtual-knot problem 30 — In we have studied a mod-2 categorification of the arrow polynomial and discovered many baffling examples of pairs of…
- Math-13247 Virtual-knot problem 31 — Make a systematic study of Vassiliev invariants for virtual knots and links.
- Math-13248 Virtual-knot problem 32 — Generalize virtual knot theory to virtual 2-spheres in 4-space.
- Math-13249 Virtual-knot problem 36 — electrical
- Math-13250 Virtual-knot problem 41 — Which quantum invariants extend to virtual knots themselves without restrictions?