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 give …

We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein
algebras of closed surfaces to L^ e's stated skein algebra associated to open surfaces. We …

The aim of this article is to study the $\operatorname {SL} _2 (\mathbb {C}) $–character
scheme of a finitely generated group. Given a presentation of a finitely generated group …

We prove that both stated skein algebras and their reduced versions at odd roots of unity are
almost-Azumaya and compute the rank of a reduced stated skein algebra over its center …

We show that the algebraic automorphism group of the SL2 (C) character variety of a closed
orientable surface with negative Euler characteristic is a finite extension of its mapping class …

For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality
between two volume forms on the space of representations of the surface in a semisimple …

We study irreducible-representations of twist knots. We first determine all non-acyclic-
representations, which turn out to lie on a line denoted as in. Our main tools are character …

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 …

For $ k\geq 0$, a $ k $-generalized Markov number is an integer which appears in some
positive integer solution to the $ k $-generalized Markov equation $ x^ 2+ y^ 2+ z^ 2+ k (yz+ …

We prove that the balanced Chekhov–Fock algebra of a punctured triangulated surface is
isomorphic to a skein algebra which is a deformation of the algebra of regular functions of …