15 problems

Let $b=\frac{2}{\beta}-1$. The hypermap series enumerates bipartite maps with independently specified profiles of the two types of vertices, and its coefficients are denoted by…

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

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 $\nu$.…

Equivalence conjecture. Every two maximal complete $1$-systems of loops on $F$ are equivalent.

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 JT gravity include non-orientable surfaces, and consider a matrix integral with the spectral curve … The matrix integral is taken in the symmetry class obtained by conjugation…

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 $\no_g$ be a non-orientable surface, let $\pmf(\no_g)$ be its space of projective measured foliations, and let $h$ be the Hausdorff dimension of the limit set of its mapping cl…

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…

Let $n$ be a positive integer and let $\pi,\sigma,\lambda\vdash n$ be partitions. Let $M^\lambda_{\pi,\sigma}$ be the set of rooted maps indexed by these partitions, and call a map…

Weighted-map interpolation conjecture. There exists a measure of non-orientability of $M$, given by a polynomial $\operatorname{weight}_M(\gamma)$ in $\gamma$, such that weighting…

Let $T$ be the $3$-twist-spun trefoil, viewed as a $2$-knot, and let $C$ be a cross-cap embedded in $4$-space. Write $T\mathbin{\#}C$ for their connected sum, and let…

An embedded projective plane in $4$-space is a smoothly embedded non-orientable surface whose non-orientable genus $g$ is the number of projective-plane connected-summands; its nor…

Let $p_g$ be the constants in the asymptotic formula for rooted maps on a non-orientable surface of type $g$, and let $u(z)=z^{1/2} sum{g=0}^{infty}ug z^{-5g/2}$ be the scaled gene…

Let $M$ be a non-orientable surface, and let $\gamma$ be a contractible simple closed curve on $M$. Baer-type conjecture. Theorem $1.1$ is true for $\gamma$, namely, the isotopy co…