206 problems

A fibration has trivial fibre transport when its fibre transport action is trivial, and a fibre is positively rationally elliptic when its rational homotopy and cohomology groups a…

Let $E^{p,q}_r(n)$ denote the unstable spectral sequence in the notation of the paper, indexed by the parameter $n$, and let ${}^V\!E^{p,q}_r$ denote the Vassiliev spectral sequenc…

The Hochschild-to-cyclic spectral sequence for an c4b1c4b7b3bcb1c4b1-algebra $A$ is … Here $A$ is smooth and proper over a field of characteristic $0$. Kontsevich–Soibelman conject…

Let $L\subset S^3$ be a link, let $\overline{OKh}(L)$ denote its reduced odd Khovanov homology, and let $\Sigma(L)$ denote the branched double-cover of $S^3$ branched along $L$. Oz…

Let $L$ be a link in $S^3$. Write $coverline{H}(L)$ and $H^-(L)$ for the reduced, middle, and unreduced HOMFLY-PT homologies of $L$, and $coverline{\operatorname{HFK}}(L)$,…

Let $G$ be a Lie group with maximal torus $T$, and let $G\to G/T$ be the quotient fibration. Write $E_r^{*,*}(G;\mathbb{Z})$ for its Leray–Serre spectral sequence, and regard…

Dunfield–Gukov–Rasmussen conjecture. There is a spectral sequence from HOMFLY-PT homology to knot Floer homology.

Ozsváth–Szabó's degeneration conjecture. All subsequent differentials in the universal coefficient spectral sequence vanish, so that its $E^\infty$ term is $HC^\infty_*(Y)$.

Rapoport–Zink spectral sequence conjecture. For all $r,w$, the induced map on $E_2$-terms is an isomorphism

Over $\mathbb{C}$, let $\eta^{-1}\mathbb{S}$ be the η-periodic motivic sphere, let $P$ and $v_n$ denote the classes on the $E_2$-page of its motivic Adams spectral sequence, and le…

Diagram-independence conjecture. The spectral sequence in Theorem 1.3 should be independent of the planar diagram $\mathcal{D}$.

Let $K_3$ be the space of long knots in $\mathbb{R}^3$, and let ${}^V\! E_r$ denote the Vassiliev spectral sequence for $K_3$ over a field $\mathsf{k}$. Vassiliev's degeneration co…

Let the Bendersky–Gitler spectral sequence be the spectral sequence associated with the nerve of the covering of the fat diagonal in $M^k$, with higher differentials…

Let $L$ be a link in $S^3$ and let $n$ be a positive integer. Write $\overline{H}_n(L)$ and $H_n(L)$ for reduced and unreduced $\mathfrak{sl}(n)$ homology, and…

Let $L$ be a link in $S^3$. The HOMFLY-PT homologies carry gradings $\operatorname{gr}_T$ and $\operatorname{gr}_M$, and the grading-shifted knot Floer homologies…

Let $(X,\mathcal E)$ be a compact non-singular real tropical hypersurface. Let ${\mathcal K}_1,\dots,{\mathcal K}_n$ and ${\mathcal S}_{\mathcal E}$ be the coefficient systems appe…

Degeneration conjecture. The spectral sequences degenerate at the $E_3$-term for any reduced plane curve $C:f=0$.

Ozsváth–Szabó's differential conjecture. The only possibly nontrivial differential in this spectral sequence is $d^3$, and this differential is given by a formula in terms of the t…

Let $K$ be a knot in $S^3$. Let $\mathcal{K}$ be an $n$-crossing braid diagram for $K$ with its outermost strand cut, and let $G_I$ for $I\in\{0,1\}^n$ be the planar trivalent grap…

Let $L$ be a link, and let $c$ and $c'$ be components of $L$. Denote by $\widetilde{E}^k(L,c)$ the reduced Szabó spectral sequence associated to $L$ with distinguished component…

Rational collapse conjecture. The spectral sequences for the pointed spaces rationally collapse in total degrees $2* \leq n-3$, while the corresponding spectral sequences for the u…

Let $F$ be a field with $|cdot F/cdot F^2|=2^n$, so that $E=E_n\cong (\mathbb Z/2)^n$, and let ${\mathcal G}_F$ be the associated $W$-group. Let…

Let $\lambda\in\mathbb C$, let ${\mathfrak{gl}}(\lambda)$ be embedded in $\mathrm{Dif}_1$, and let … be the first page of the associated Feigin Serre–Hochschild spectral sequence.…

Feigin's degeneration conjecture. This spectral sequence degenerates at $E_2$. The conjecture is part of Feigin's proposed description of the cohomology of $\mathrm{Dif}_1$; the so…

The $G^1$-degeneration conjecture. The spectral sequence $G^k_{p,q}$ for $H_*(X(\mathbb{R}))$ degenerates at the $G^1$ level.