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Relating quantum character varieties and skein modules (2211.04252v1)
Published 8 Nov 2022 in math.QA and math.AT
Abstract: We relate the Kauffman bracket stated skein modules to two independent constructions of quantum representation spaces of Habiro and Van der Veen with the second author. We deduce from this relation a description of the classical limit of stated skein modules, a quantum Van Kampen theorem and a quantum HNN extension theorem for stated skein modules and obtain a new description of the skein modules of mapping tori and links exteriors.