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-5801 Problem 5.25 — (Presentation for level L structures).
- Math-5802 Question 6.2 — (Rigidity of the Mod g,1 action on S1).
- Math-5803 Problem 7.3 — Compute L(Modg) explicitly for small g≥ 2.
- Math-5804 Question 7.4 — Is there a unique (up to conjugacy) minimal dilation pseudo-Anosov in Modg?
- Math-5805 Problem 7.5 — (Shortest Teichm¨ uller loop in a stratum).
- Math-5806 Problem 4.6 — Compute H • ∞(T c 3 ).
- Math-5807 Question — What is the growth rate of dW (tn, 1)?
- Math-5808 Problem 2.4 — Let Γ be a subgroup of finite index in the mapping class group Mod1,2 and let φ: Γ → Γ be an automorphism.
- Math-5809 Problem 2.13 — (a) It is known from [33] that H2(Mod3; Z) and H2(Mod1 3; Z) are either Z or Z⊕ Z2.
- Math-5810 Problem 3.1 — (a) Is it possible to generate the mapping class group of a closed nonori- entable surface by two elements?
- Math-5811 Problem 3.3 — .
- Math-5812 Problem 2 — Given a tuple ×N i=1(mi,ti) ∈ ZN, give a tractable expression in terms of Dehn- Thurston or other coordinates for the…
- Math-5813 Problem 10 — Though the (virtual) Euler characteristics are already known [28,56], devise a matrix model using screens to calculat…
- Math-5814 Question — Do there exist any other examples of non commuting homeomorphisms g andh which are not both Dehn twists and satisfy a…
- Math-5815 Question — Does there exist a set of at least three pseudo-Anosov homeomorpisms such that every pair satisfies a braid relation.
- Math-5816 Question (Smith) — Let αi, i = 1,...,n be a configuration of curves on a surface S of genus g with one boundary component δ such that ev…
- Math-5817 Question — Consider the Artin group A5 (the braid group on six strings) divided by the relation (a1a2a3a4)5 = a5a4a3a2a2 1a2a3a4a5.
- Math-5818 Problem 2.1 — Assume, for this problem, that M is a 3-manifold with non-empty boundary.
- Math-5819 Problem 2.4 — Knowing that d(φ)≤ 1, can we decide whether d(φ) = 0?
- Math-5820 Problem 2.7 — Study the handlebody subgroup of Mg.
- Math-5821 Problem 2.8 — Recall that we noted, earlier, that every genus g Heegaard splitting of every homology 3-sphere is obtained by allowi…
- Math-5822 Problem 2.11 — Hempel’s distance function was chosen so that it would capture the geometry, and indeed it does that very well, yet i…
- Math-5823 Problem 2.13 — In [43] it is proved that in the case of the trivial genus g surface bundle, i.e.
- Math-5824 Problem 3.1 — Study, systematically and with the help of computers, the finite quotients of Mg which do not factor through Sp (2g, Z).
- Math-5825 Problem 3.2 — Construct any representations of Mg, finite or infinite, which do not factor through Sp(2g, Z).
- Math-5826 Problem 3.4 — Find a candidate for a faithful finite-dimensional matrix representation of Mg orMg,1,0.
- Math-5827 Problem 3.7 — Are there quotients of Ig orKg in which the intersection of either Ig orKg with the handlebody group Hg is sufficiently…
- Math-5828 Problem 2.5 — Construct an example of a pseudo-Anosov mapping class for a closed surface which is not ergodic on the SU(2)-characte…
- Math-5829 Problem 6 — (Purely cyclic).
- Math-5830 Problem 21 — (Exceptional Strata).
- Math-5831 Problem 3.5 — Is every finite rank subgroup of Whittlesey’s group a Schottky subgroup of MCG (S)?
- Math-5832 Problem 3.6 — Give examples and constructions of virtual Schottky subgroups of MCG (S).
- Math-5833 Question 5 — Is there a homological definition of representations of the Birman-Wenzl- Murakami algebra?
- Math-5834 Question 6 — DoesX3 equal 0 in Zn?
- Math-5835 Question 2.6 — If there is a homomorphism from a subgroup of finite index in Aut(Fn) onto a subgroup of finite index in GL(m, Z), th…
- Math-5836 Question 2.9 — Fix a basis for Fn and let An−1⊂ Aut(Fn) be the copy of Aut(Fn−1) corre- sponding to the first n− 1 basis elements.
- Math-5837 Question 3.6 — Is there a map Out(Fn)→ Out(Fm) that induces an isomorphism on homology in the stable range?
- Math-5838 Question 5.4 — Is the image of the second Morita class in H8(GL(6, Z); Q)) non-trivial?
- Math-5839 Problem 3.5 — Find explicit way of calculating d1(ϕ) for any given element ϕ ∈ Kg.
- Math-5840 Problem 4.3 — Produce non-trivial rational (co)homology classes of OutFn.
- Math-5841 Problem 4.5 — Prove (or disprove) that the natural homomorphism H 4(OutF4; Q)∼= Q−→H 4(IOut4; Q)GL is an isomorphism where the righ…
- Math-5842 Problem 4.6 — Determine the homomorphisms H 8(M3,∗; Q) i∗ ←−H 8(OutF6; Q) p∗ ←−H 8(GL(6, Z); Q) (10) induced by the above homomorph…
- Math-5843 Problem 10.3 — Give examples of odd valent graphs Γ whose associated homology classes Φ(Γ)∈ H∗(OutFn; Q) are non-trivial as many as…
- Math-5844 Major problems 10 — Once again, I am not sure whether this problem deserves to be called major, but it is annoying that th…
- Math-5845 Morava K- and E-theory 7 — Presumably one should be able to form a category of E-S module spectra; spectra with an action of the…
- Math-5846 Applications 4 — Stefan Stolz showed that a simply connected Spin manifold of dimension at least 5 admits a metric of p…
- Math-5847 Applications 6 — Improve on Benson-Carlson-Rickard.
- Math-5848 Axiomatic stable homotopy 7 — The equivariant stable homotopy category is not treated very well in our memoir.
- Math-5849 Model categories 1 — The safest sort of problem to work on with model categories is building one of interest in applications.
- Math-5850 Model categories 5 — The second step: show that the category of algebras over a cofibrant operad admits a model structure,…