5 problems

Let $T$ be a framed oriented $r$-component tangle in ${\mathbb{R}}^3_{x\geq 0}$, let $N(\varLambda_T)$ be its specified neighborhood, and let $H$ denote the reference subspace used…

Framed cord algebra conjecture. The framed cord algebra is the zero-th relative contact homology of $\Lambda_K$ in $ST^*M$.

Finite-generation characterization. The algebra $HC_0(K;l)$ is finitely generated as an $R$-algebra if and only if $K$ is not local.

Ng's conjecture. The cord algebra invariant of $K$ is the $0$-th relative knot contact homology.

Finite-generation conjecture. Framed cord algebras are always finitely generated for non-local knots.