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The quantum trace as a quantum non-abelianization map

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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