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The skein algebra of arcs and links and the decorated Teichmüller space. (English) Zbl 1290.53080

This paper extends the notion of skein algebra for a punctured surface and relates this notion to geometric structures. Let us recall that the skein module was introduced independently by Turaev and Przytycki as a generalization of the Jones polynomial of a link in \(S^3\). In this work, the authors include arcs in the definition of the skein algebra and define a generalized link.

MSC:

53D55 Deformation quantization, star products
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
17B63 Poisson algebras
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