9 problems

Let $f:\mathbb{R}^4\to\mathbb{R}^2$ be a polynomial map with an isolated singularity at the origin, meaning that $f(0)=(0,0)$, its first derivatives vanish at the origin, and its J…

Let $L$ be a fibered link in $S^3$. A simple branched cover is a map $\pi\colon S^3\to S^3$ branched over a link $L'$, and $\alpha$ and $\beta$ are unknots that are braid axes of…

Let $L$ be a link in $S^3$, and let its fiber surface be the page of a fibration of its complement over $S^1$. A Hopf plumbing or deplumbing is the operation of adding or removing…

Let $L$ be a link, let $C_L$ be its exterior, and let $\xi:\pi_1C_L\to\mathbf{Z}$ be the homomorphism sending each meridian generator to $1$. Let $\Lambda$ be the group ring of…

Let $f$ be a mapping with an isolated critical point at $\boldsymbol{x}$. For $\boldsymbol{p},\boldsymbol{q}in S^2$ with $\boldsymbol{p}\ne\boldsymbol{q}$, Hypothesis 3.8 requires…

Let $L$ be a fibered link in $S^3$. A mutual arc presentation is the presentation defined in the paper that generalizes Cromwell's arc presentations. Mutual arc presentation conjec…

Let $L$ be a fibered link in $S^3$. A braided open book is an open book in $S^3$ whose binding is braided relative to the standard open book with unknotted binding; equivalently, i…

A real polynomial map $f\colon \mathbb{R}^4\to\mathbb{R}^2$ has an isolated singularity at the origin when its singular locus near the origin is just $\{0\}$. Its link is the link…

General Milnor conjecture. If $\xi_L$ is tight, then $\Sigma$ maximizes Euler characteristic among all such surfaces.