14 problems

Let Khovanov homology be the homological invariant of links categorifying the Jones polynomial, and let link cobordisms be smooth cobordisms between links. Khovanov's functoriality…

For any link, let $\mathcal{F}(L)$ be the foam-based bigraded complex and let $\operatorname{KR}(L)$ be the KhovanovRozansky complex. Suppose the already established isomorphism be…

Let $S$ be a compact oriented surface and let $J,\widetilde J$ be representations of $S$ by sequences of link diagrams, with endpoint diagrams $J_0,J_1$ and…

Let $\mathcal A$ be the category of $\mathbb Z[1/2]$-modules. Let ${\bf\mathcal Cob}_f^4$ be the category of colored framed link diagrams and movie presentations of colored framed…

A colored link is a link whose components are assigned natural-number colors, and Khovanov and Lee homology theories are obtained by applying the functors…

Cobordism invariance conjecture. The induced maps on cohomology give an invariant of framed colored link cobordisms.

Let $\Sigma$ be a link cobordism, and let two movies of $\Sigma$ have corresponding source and target link diagrams that are isomorphic. Each movie induces a map on the homology gr…

Let Putyra's generalized Khovanov bracket be the link homology theory that specializes to both even and odd Khovanov homology. Let smooth link cobordisms be the morphisms between l…

Khovanov's isotopy invariance conjecture. Up to sign, $\operatorname{Kh}(\Sigma)$ is invariant under isotopy of $\Sigma$ relative to $\partial\Sigma$. The conjecture establishes th…

Let $\Sigma$ be a link cobordism, and let a presentation of $\Sigma$ as a sequence of elementary cobordisms induce a map of spectra between the stable homotopy types associated to…

Let $L_0$ and $L_1$ be links in ${\mathbbm R}^3$, and let $\Sigma:L_0\longrightarrow L_1$ be a link cobordism in ${\mathbbm R}^3\times[0,1]$, represented by a sequence of Reidemeis…

Let $W_0,W_1\subset S^3\times[0,1]$ be embedded cobordisms between links $L_0\subset S^3\times\{0\}$ and $L_1\subset S^3\times\{1\}$, and let…

Grid-diagram agreement conjecture. The maps described in terms of grid diagrams by Sarkar and Ozsváth–Stipsicz–Szabó are equal to the maps defined in this paper for elementary link…

Let ${\mathcal Cob}_{f/i}^4$ be the quotient of ${\mathcal Cob}_f^4$ by framed movie moves. Assume the chain transformations in the Lee functor construction are made canonical, ind…