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-13301 Problem 3.5 — Study homomorphisms Modg→ Mod(N ) and Mod(N )→ Modg.
- Math-13302 Problem 4.2 — .
- Math-13303 Question 4.3 — .
- Math-13304 Question 4.4 — .
- Math-13305 Problem 1 — Understand either classically or as quantum geometric objects the non-Hausdorff quotients of PL 0(F ) or PL(F ) by MC…
- Math-13306 Problem 3 — Give a useful (piecewise) tropical description of the two elementary transformations.
- Math-13307 Problem 4 — Does the recipe in Theorem 4 give virtually all pA maps?
- Math-13308 Problem 6 — Calculate the topological type (PL-homeomorphism, homotopy, homology...
- Math-13309 Problem 7 — Devise a matrix model (cf.
- Math-13310 Problem 8 — [Contributed by the referee] Does Theorem 5 say anything about the structure of the end of Riemann’s moduli space?
- Math-13311 Problem 11 — [LevelN Torelli Franchetta Problem] What is the second cohomology group of the levelN Torelli group?
- Math-13312 Problem 12 — Calculate various group-theoretic boundaries of mapping class and Torelli groups, for instance, Tits boundaries.
- Math-13313 Problem 13 — What are the kernels of the Magnus representations?
- Math-13314 Question (Smith) — What is the maximal length of such a product?
- Math-13315 Question 2.2 — (Donaldson).
- Math-13316 Problem 1.1 — The ideas which were just described relate to the beginning of the lower central series of Ig.
- Math-13317 Problem 2.2 — How is the Nielsen-Thurston trichotomy related to the question of whether the distance is 0, 1, 2 or≥ 3?
- Math-13318 Problem 2.5 — Knowing that d(φ)≥ 1, can we decide whether it is ≥ 2?
- Math-13319 Problem 2.9 — Uncover the structure in the mapping class group that relates to the classifica- tion theorem for the Heegaard splitt…
- Math-13320 Problem 2.10 — Given a normal subgroup Gg ofMg, what basic properties are needed in a complex G(Sg) of curves on Sg so that Mg will…
- Math-13321 Problem 2.14 — A 3-manifold is fibered if it admits a surface bundle structure.
- Math-13322 Problem 3.5 — Is there a natural quotient complex of any one of the complexes discussed in §1 which might be useful for the constru…
- Math-13323 Problem 1 — Develop techniques to describe the sets Cχ,θ.
- Math-13324 Problem 2 — Show that the inclusion of Proposition 5 is a bijection.
- Math-13325 Problem 1.1 — Investigate the dependence of Expρ,⟨f,M ⟩ on the marked Riemann surface ⟨f,M⟩.
- Math-13326 Conjecture 2.1 — Let Ω∗(Hom(π,G )/G) be the de Rham algebra consisting of all measurable differential forms on Hom(π,G )/G.
- Math-13327 Conjecture 2.2 — Suppose C∞(Hom(π,G )/G) D− →C∞(Hom(π,G )/G) is a differential operator which commutes with the ModΣ-action on Hom(π,G…
- Math-13328 Problem 2.2 — Decompose the representation on H0 into irreducible representations of ModΣ.
- Math-13329 Problem 2.3 — Find a similar geometric interpretation for the irreducible constituents for compact nonabelian groups G.
- Math-13330 Conjecture 3.1 — Suppose that b = 0 (Σ is closed).
- Math-13331 Problem 3.2 — Find general conditions which ensure that (10) is proper.
- Math-13332 Problem 3.3 — Determine the ergodic behavior of the ModΣ-action on the level sets ( iR× R×iR ) ∩κ−1(t) wheret> 2.
- Math-13333 Conjecture 3.2 — If k = 1, then U is onto.
- Math-13334 Problem 1: — Determine the metric completion of the Gromov boundary of C(S) and relate this metric completion to the geometry of C…
- Math-13335 Problem 3 — (Renormalization of billiards in polygons).
- Math-13336 Problem 7 — (Algorithm for Veech groups).
- Math-13337 Problem 12 — (Analog of Ratner theorem).
- Math-13338 Problem 13 — (Kernel foliation).
- Math-13339 Problem 16 — (Dynamical Hodge decomposition).
- Math-13340 Problem 1.1 — Given a subgroup G <MCG (S), how is the geometry of ΓG related to the dynamics of the action of G on Thurston ’s comp…
- Math-13341 Problem 2.2 — Does the converse hold in the above theorem without the assumption that G is free?
- Math-13342 Problem 3.3 — Does there exist an algorithm which produces the integer M in Theorem 3.1, given φ1,...,φ n?
- Math-13343 Problem 4.4 — Does there exist a simple cycle of dihedral subgroups of MCG (S) so that the associated reflection group P injects in…
- Math-13344 Problem 5.4 — Suppose that G <MCG (S) is a finite co-area Veech subgroup.
- Math-13345 Problem 6.1 — Are the Leininger–Reid subgroups geometrically finite, with cusp groups the reducible cyclic subgroups?
- Math-13346 Problem 6.2 — If G< MCG (S) is geometrically finite with cusp groups H1,...,H n, what can be said about the geometric properties of…
- Math-13347 Question 3.3 — LetG∼=π1(S2g)→ Γg be the injection given by Theorem 3.1.
- Math-13348 Question 3.4 — Is Γg GFERF for g≥ 2?
- Math-13349 Question 4.9 — Does there exist a cocompact Fuchsian subgroup of ∆5 that misses the com- pactification locus?
- Math-13350 Question 1 — If R = Q(q1,q 2), is the above map from Bn toHn(q1,q 2) injective?