| Texto completo | |
| Autor(es): |
Korinman, J.
;
Quesney, A.
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS; v. 31, n. 06, p. 49-pg., 2022-05-01. |
| Resumo | |
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) | |
| Processo FAPESP: | 18/19603-0 - Teoria de Homotopia e de Raizes, Topologia de Variedades, Espaços Estratificados, Formas Espaciais Esféricas e Sistemas Dinâmicos Topológicos. |
| Beneficiário: | Alexandre Thomas Guillaume Quesney |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |