## 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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