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

Roger, Julien; Yang, Tian

J. Differ. Geom. 96, No. 1, 95-140 (2014).

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.

Reviewer: Angela Gammella-Mathieu (Metz)

MSC:

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

Keywords:

deformation quantization; Poisson algebra; hyperbolic geometry; geodesic lengths functions