Article Dans Une Revue Algebraic and Geometric Topology Année : 2024

Classical shadows of stated skein representations at roots of unity

Résumé

We extend some results of Bonahon, Wong, Bullock and Turaev concerning the skein algebras of closed surfaces to Lê’s stated skein algebras associated to open surfaces. We prove that the stated skein algebra with deforming parameter C1 embeds canonically into the center of the stated skein algebra whose deforming parameter is an odd root unity. We also construct an isomorphism between the stated skein algebra at C1 and the algebra of regular functions of the relative SL2–character variety of the surface. As a result, we associate to each isomorphism class of irreducible or local representations of the stated skein algebra an invariant which is a point in the relative character variety.

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hal-05078759 , version 1 (22-05-2025)

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Julien Korinman, Alexandre Quesney. Classical shadows of stated skein representations at roots of unity. Algebraic and Geometric Topology, 2024, 24 (4), pp.2091-2148. ⟨10.2140/agt.2024.24.2091⟩. ⟨hal-05078759⟩
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