5 papers
Triangular decomposition of character varieties
Julien Korinman
A marked surface is a compact oriented surface equipped with some pairwise disjoint arcs embedded in its boundary. In this paper, we extend the notion of character varieties to mar…
Azumaya loci of skein algebras
Hiroaki Karuo, Julien Korinman
We compute the Azumaya loci of Kauffman-bracket skein algebras of closed surfaces at odd roots of unity and provide partial results for open surfaces as well. As applications, we g…
Skein modules of closed 3 manifolds define line bundles over character varieties
Julien Korinman
Let M be a closed 3-manifold and S(M) the skein module of M at some odd root of unity. Using the Frobenius morphism, we can see S(M) as the space of global sections of a coherent s…
A survey on mapping class group representations derived from skein theory
Julien Korinman
We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.
Quantum holonomic link invariants derived from stated skein algebras
Julien Korinman
We define invariants for a framed link equipped with a SL2 local system in its complement and additional combinatorial data based on the theory of representations of stated skein a…