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Azad, Farhan; Chen, Zixi; Dreyer, Matt; Horowitz, Ryan; Moon, Han-Bom

Presentations of the Roger-Yang generalized skein algebra. (English) Zbl 1481.57025

Algebr. Geom. Topol. 21, No. 6, 3199-3220 (2021).
The Roger-Yang generalized skein algebra is a quantization of the decorated Teichmüller space. Its definition generalizes the construction of the Kauffman bracket skein algebra which was introduced independently by Turaev and Przytycki, based on Kauffman’s skein-theoretic description of the Jones polynomial. The main result in the paper under review is a presentations of the Roger-Yang generalized skein algebras for punctured spheres with an arbitrary number of punctures. Such presentations were known for genus \(0\) with at most three punctures and for genus 1 with \(0\) or \(1\) puncture. At the same time, the authors obtain a new interpretation of the homogeneous coordinate ring of the Grassmannian of planes in terms of skein theory.
Reviewer: Athanase Papadopoulos (Strasbourg)

MSC:

57K31 Invariants of 3-manifolds (including skein modules, character varieties)
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
57M50 General geometric structures on low-dimensional manifolds

Keywords:

skein algebra; punctured sphere; ring presentation
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References:

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