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-13251 Virtual-knot problem 45 — To prove that the invariant $\mathcal{F}$ constructed by V.
- Math-13252 Virtual-knot problem 49 — Turaev constructed the map from the set of long flat knots to the set of long virtual knots.
- Math-13253 Virtual-knot problem 50 — The problem about cobordisms in sections: Let us have a free knot and its cobordism.
- Math-13254 Virtual-knot problem 52 — If $X$ is the free rack, is $\Gamma X$ a cat(0) space?
- Math-13255 Virtual-knot problem 54 — Can one construct a projection from the set of graph-links to the set of realizable graph-links?
- Math-13256 Virtual-knot problem 55 — Construct a parity on graph-links by using Bouchet's criterion about the realizability of a graph.
- Math-13257 Virtual-knot problem 58 — Construct a group for graph-links which is analogous to the group from .
- Math-13258 Virtual-knot problem 59 — Construct “graph-braids”.
- Math-13259 Problem 1E — What are the obstructions to the realization of these chains of formal changes by paths in the paramet…
- Math-13260 Problem 2A — What is the minimal number of open sets $U_{i}$ covering ${\mathbb{R}}^{6}$ such that for any $U_{i}$…
- Math-13261 Problem 2B — The same questions concerning the approximate solutions.
- Math-13262 Problem 3 — Is the complement of the essential ramification set in ${\mathbb{R}}^{d}$ a $K(\pi,1)$-space?
- Math-13263 Problem 4 — Are these geometric obstructions sufficient to solve the above problem?
- Math-13264 Problem 5A — Is it true that any hypersurface from the space $P(d;N)$ can be connected with a trivial one by a gene…
- Math-13265 Problem 5B — A version of the previous problem, in which the complexity measure is not purely topological: namely,…
- Math-13266 Problem 5C — Give an upper bound for the function $T\mapsto F$.
- Math-13267 Problem 6A — Is it true that any real Morsification of $f$ can be connected with one of complexity $\rho(f)$ by a g…
- Math-13268 Problem 6B — What can be said about the number $\rho(f)$?
- Math-13269 Problem 7 — Give a similar universal estimate of the radius of convergence for multidimensional Newton’s method of…
- Math-13270 1.2 (Choi) — Convex projective deformations from a CR structure
- Math-13271 2.1 (Leitner) — Limits between Thurston geometries
- Math-13272 4.3 (Cooper) — 3-manifold groups acting on the affine building for $SL(4,\mathbb{R})$
- Math-13273 6.2 (Maher) — Random tetrahedron-gluing pseudomanifolds
- Math-13274 6.3 (Maher) — Structure behind Rivin's experimental regularity
- Math-13275 Problem 1.1 — Study the function Ψ: Mg→ [−log(µg),∞) as a (rational) Morse function.
- Math-13276 Problem 2.2 — Letγ1,···,γ 2g be the standard basis of Z2g.
- Math-13277 Problem 2.3 — Work out the details of this construction of the completion Yg of Yg.
- Math-13278 Problem 4.1 — Show that there are many quasihomomorphisms f:MCG (Sg)→ R that satisfy (1) and (2) above plus (3) f is bounded on eve…
- Math-13279 Problem 2.2 — Compute CommModg (Γ) for various subgroups Γ< Modg.
- Math-13280 Problem 2.3 — (Volume spectrum).
- Math-13281 Problem 2.14 — Give a proof of Theorem 2.13 which does not depend on the classification of finite simple groups.
- Math-13282 Problem 2.16 — (Automorphism groups with special properties).
- Math-13283 Question 3.14 — (Rational growth for properties).
- Math-13284 Conjecture 4.6 — LetS be any surface with d(S)≥ 1.
- Math-13285 Problem 4.12 — (Distortion of the Schottky locus).
- Math-13286 Conjecture 5.5 — For each k≥ 1, the group (Ig)k is not finitely generated.
- Math-13287 Problem 5.19 — Give an elementary, purely combinatorial-topological and group-theoretic, proof of Hain ’s theorem.
- Math-13288 Problem 5.21 — (Malcev mod 2).
- Math-13289 Question 7.6 — Does spec(Ig(k)) have bounded multiplicity for k≥ 3?
- Math-13290 Question 7.7 — (Simple length spectrum).
- Math-13291 Question 7.12 — For various subgroups H <Modg, compute the density of spec(H) in spec(Modg) and the density of H∩Pg inPg.
- Math-13292 Problem 4.1 — ( Topological Schottky Problem).
- Math-13293 Problem 4.3 — Determine good bounds for the homological dimension (or the CW-dimension) ofT c g.
- Math-13294 Problem 4.5 — Try to understand the “topology at infinity” of T c g.
- Math-13295 Problem 4.9 — Investigate the topology of Hg andHc g and their components.
- Math-13296 Question I — s it true that any normal subgroup is commensurable with such a subgroup?
- Math-13297 Question — Are there any other relations between N -th powers Tγ = tN γ of Dehn twists for sufficiently high N?
- Math-13298 Conjecture — For every finitely generated subgroups G of ModS, the group Φf (G) is nilpotent.
- Math-13299 Problem 2.10 — Compute ϕ(g,n ).
- Math-13300 Problem 2.11 — Let g≥ 3 and b≥ 1.