5 problems

Let $\ell$ be the vertical degree parameter in the homological representation functors for mapping class groups of orientable and non-orientable surfaces. The arguments under discu…

Let $S$ be a surface, and let $\mathfrak{L}^{\star}_{(\mathbf{k},\ell)}(S)$ denote the relevant homological representation functor, with…

Generalized Kohno equivalence. There is an open dense subset $U\subset\mathbb{C}\times\mathbb{C}^*$ such that, whenever $(\lambda,\kappa)\in U$, the monodromy representation…

Let $\Sigma$ be an oriented surface of finite type, and let $\phi\in\operatorname{Mod}(\Sigma)$ be an infinite-order mapping class. The paper proves the corresponding assertion whe…

Let $\phi$ be a pseudo-Anosov mapping class with dilatation $\lambda$. For each finite cover $\pi$, let $\sigma(\pi)$ be the spectral radius of the homological representation…