6 problems

Let $M$ be a closed $3$-manifold, let $H_1(M)$ denote its first homology group, and let $N$ be the symplectic-fermion parameter appearing in the Lyubashenko invariant…

Let $SF_d^+$ be the even subalgebra of the symplectic fermion vertex operator superalgebra $SF_d$, and let $\mathcal{S}\mathcal{F}_d$ be the braided tensor category constructed by…

Let $\mathcal{V}_{\mathrm{ev}}(N)$ be the even part of the super-vertex operator algebra of $N$ pairs of symplectic fermions, with central charge $c=-2N$. Let $\mathsf{Q}(N,\beta)$…

Let $\mathcal{V}_{\mathcal{SF}_n^{\mathrm{even}}}$ be the even part of the vertex superalgebra of $n$ pairs of symplectic fermions, and let $\mathcal{C}_0\oplus\mathcal{C}_1$ be th…

Let $\mathcal{S}\mathcal{F}(\mathfrak{h})$ be the finite ribbon category associated with symplectic fermions and let $\operatorname{Rep}(\mathcal{V}_{\mathrm{ev}})$ be the represen…

Braided equivalence conjecture. For $\beta=e^{-\pi i d/8}$, the functor $F$ is a $\mathbb{C}$-linear braided monoidal equivalence. This conjecture identifies the representation cat…