| Full text | |
| Author(s): |
Korinman, J.
;
Quesney, A.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS; v. 31, n. 06, p. 49-pg., 2022-05-01. |
| Abstract | |
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 some abelian character variety. We first deduce from this observation a classification of the irreducible representations of the balanced Chekhov-Fock algebra at odd roots of unity, which generalizes to open surfaces the classification of Bonahon, Liu and Wong. We re-interpret Bonahon and Wong's quantum trace map as a non-commutative deformation of some regular morphism between this abelian character variety and the SL2-character variety. This algebraic morphism shares many resemblances with the non-abelianization map of Gaiotto, Moore, Hollands and Neitzke. When the punctured surface is closed, we prove that this algebraic non-abelianization map induces a birational morphism between a smooth torus and the relative SL2 character variety. (AU) | |
| FAPESP's process: | 18/19603-0 - Homotopy and root theory, manifold theory, stratified spaces, spherical space forms and topological dynamic systems. |
| Grantee: | Alexandre Thomas Guillaume Quesney |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |