6 problems

Let $j\geq1$ and set $n=j+2$. Then $\pi_0\operatorname{Emb}(D^j,D^n)$ is the set of isotopy classes of codimension-two disk embeddings, and the invariant … has the indicated target…

Let $m$ lines in the plane intersect in a single point, and let $b4_n$ denote the associated invariant for the arrangement, with $n\geq 0$. Conjecture. For every $n\geq 0$, … This…

Let $M$ be a $3$-manifold, let $\pi_1(M)_{r}^{(n)}$ denote the $n$th term of its rational derived series, and define … For each $n\in\mathbb{N}$, let $||\\,\cdot\\,||_n$ be the cor…

Existence conjecture. For each $n\geq 0$ there exist knots $K$ and $K_*$ such that $\mathcal{A}_i(K)\cong\mathcal{A}_i(K_*)$ for $0\leq i<n$, but

Let $L$ be an oriented link as in the zero-twist theorem, and let $L(q)$ denote the link obtained by the prescribed $1/q$-surgery or twisting operation. Let $\Delta_{L(q)}$ be its…

Let $L\subset\mathbb S^3$ be an oriented link with vanishing Alexander polynomial $\Delta_L$, and let the higher Alexander polynomials be the successive divisors in the Alexander p…