5 problems

For all $n,f\geq 1$ and partitions $\nu\vdash 2n$, let $c_{\mu,\nu,n}(b)$ denote the coefficient associated with maps having $n$ edges and vertex and face profiles $\mu$ and $\nu$.…

For a positive torus knot $T(3,6n+1)$, let $(e,h)$ denote the normal Euler number and non-orientable genus of a smoothly and properly embedded surface in $D^4$ bounded by the knot.…

Let $\no_g$ be a non-orientable surface with $g\geq 4$. Let $\pmf^+(\no_g)$ be the space of projective measured foliations on $\no_g$ containing no one-sided leaves, and let…

Let $k\geq 1$ and let $\lambda,\mu^0,\ldots,\mu^k$ be partitions of size $n\geq 1$. A connected rooted $k$-constellation with profile $(\lambda,\mu^0,\ldots,\mu^k)$ is denoted by…

Strong Neuwirth conjecture. There exists an essential non-orientable spanning surface for $K$.