Top Open Problems
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-5751 Problem 12.23 — (A.
- Math-5752 Problem 12.24 — (A.
- Math-5753 Conjecture 12.26 — (V.
- Math-5754 Virtual-knot problem 2 — Flat Virtuals
- Math-5755 Virtual-knot problem 4 — Virtuals and the Theory of Doodles
- Math-5756 Virtual-knot problem 8 — Virtual Biquandle
- Math-5757 Virtual-knot problem 9 — Virtual braids
- Math-5758 Virtual-knot problem 12 — Virtual Quandle Homology
- Math-5759 Virtual-knot problem 14 — Brauer algebra
- Math-5760 Virtual-knot problem 17 — Crossing number problems
- Math-5761 Virtual-knot problem 22 — The Rack Space
- Math-5762 Virtual-knot problem 26 — surface arrow invariant
- Math-5763 Virtual-knot problem 27 — Study concordance and cobordism invariants of virtual knots.
- Math-5764 Virtual-knot problem 28 — Biquandles
- Math-5765 Virtual-knot problem 29 — Khovanov homology for virtual knots and links works directly with mod-$2$ coefficients.
- Math-5766 Virtual-knot problem 38 — The Kauffman bracket polynomial of a virtual diagram can have the leading term, i.e., the term having the highest pos…
- Math-5767 Virtual-knot problem 39 — We still do not know whether the free knot whose Gauss diagram is a heptagon (i.e.
- Math-5768 Virtual-knot problem 40 — Given a chord diagram $D$ we can construct the following formal chain complex.
- Math-5769 Virtual-knot problem 42 — One can consider braids with even numbers of strands.
- Math-5770 Virtual-knot problem 43 — In his wonderful paper , which firstly had the title “Knot Floer Homotopy”, Sarkar constructs a cell complex.
- Math-5771 Virtual-knot problem 46 — In it was showed how one could determine non-invertibility of long virtual knots and non-commutativity of long virtua…
- Math-5772 Virtual-knot problem 48 — The functorial mapping was constructed, by means of it we constructed the map from the set of virtual knots to the se…
- Math-5773 Virtual-knot problem 51 — Prove or disprove the conjecture about the non-uniqueness of minimal representative of a free link, i.e.
- Math-5774 Virtual-knot problem 56 — Construct generalizations of the Frobenius extension and the Rasmussen for “rigid” graph-links with orientable atoms.
- Math-5775 Virtual-knot problem 57 — Is it true that two equivalent realizable graph-links are equivalent in the class of realizable graph-links?
- Math-5776 Problem 1C — Are there more refined restrictions to the collision of critical values?
- Math-5777 Problem 1D — Give more general lower bounds of the dimension of $\mu=const$ strata in terms of intersection forms o…
- Math-5778 Problem 1F — Is there any convenient topological characteristic of the function $f_{-\varepsilon}$ which allows to…
- Math-5779 1.4 (Danciger) — Convex projective structures on glued figure-eight complements
- Math-5780 2.2 (Cooper) — An invariant polynomial on a tensor product
- Math-5781 2.3 (Cooper) — Hausdorff limits of conjugates of an isometry group
- Math-5782 3.8 (Agol) — Twisted homology products after cutting along a surface
- Math-5783 4.2 (Futer) — The surface subgroup conjecture for cubulated hyperbolic groups
- Math-5784 5.4 (Agol) — Virtual CAT(0) cubical manifold models
- Math-5785 5.7 (Agol) — Renormalized volume as a metric
- Math-5786 5.11 (Futer) — A combinatorial model with explicit bilipschitz constants
- Math-5787 5.19 (Walsh) — Limit sets of graph Kleinian groups
- Math-5788 6.1 (I. Kapovitch) — Random walks and generic pseudo-Anosov singularities
- Math-5789 7.2 (Long) — Clique numbers in unit- and prime-difference graphs
- Math-5790 7.3 (Manning) — Number fields as trace fields
- Math-5791 8.8 (Taylor) — Hyperbolic knots not arising from complicated bands
- Math-5792 Question 2.8 — (Normal subgroups).
- Math-5793 Problem 2.15 — (Frequency of low symmetry).
- Math-5794 Problem 2.19 — (Canonical basepoints for Mg).
- Math-5795 Question 2.20 — (Number of Hurwitz surfaces).
- Math-5796 Question 3.1 — (Fast word problem).
- Math-5797 Problem 3.10 — Find a finitely presented subgroup H < Modg for which there are infinitely many conjugacy classes of finite subgroups…
- Math-5798 Conjecture 4.2 — ( Mg is maximal).
- Math-5799 Problem 5.8 — (Sharp bounds for involution generating sets).
- Math-5800 Problem 5.23 — Compute H1(Modg[L]; Z).