Character varieties
A Sikora - Transactions of the American Mathematical Society, 2012 - ams.org
We study properties of irreducible and completely reducible representations of finitely
generated groups $\Gamma $ into reductive algebraic groups $ G. $ In particular, we study …
generated groups $\Gamma $ into reductive algebraic groups $ G. $ In particular, we study …
Stated skein algebras of surfaces
F Costantino, TTQ Lê - Journal of the European Mathematical Society, 2022 - ems.press
Stated skein algebras of surfaces Page 1 © 2022 European Mathematical Society Published by
EMS Press and licensed under a CC BY 4.0 license J. Eur. Math. Soc. 24, 4063–4142 (2022) …
EMS Press and licensed under a CC BY 4.0 license J. Eur. Math. Soc. 24, 4063–4142 (2022) …
Triangular decomposition of skein algebras
TTQ Lê - Quantum Topology, 2018 - ems.press
By introducing a finer version of the Kauffman bracket skein algebra, we show how to
decompose the Kauffman bracket skein algebra of a surface into elementary blocks …
decompose the Kauffman bracket skein algebra of a surface into elementary blocks …
Skein algebras of surfaces
J Przytycki, A Sikora - Transactions of the American Mathematical Society, 2019 - ams.org
We show that the Kauffman bracket skein algebra of any oriented surface $ F $(possibly with
marked points in its boundary) has no zero divisors and that its center is generated by knots …
marked points in its boundary) has no zero divisors and that its center is generated by knots …
SU (3)-skein algebras and webs on surfaces
C Frohman, AS Sikora - Mathematische Zeitschrift, 2022 - Springer
The SU 3-skein algebra of a surface F is spanned by isotopy classes of certain framed
graphs in F× I called 3-webs subject to the skein relations encapsulating relations between …
graphs in F× I called 3-webs subject to the skein relations encapsulating relations between …
Azumaya loci of skein algebras
H Karuo, J Korinman - arXiv preprint arXiv:2211.13700, 2022 - arxiv.org
We compute the Azumaya loci of Kauffman-bracket skein algebras of closed surfaces at odd
roots of unity and provide partial results for open surfaces as well. As applications, we give …
roots of unity and provide partial results for open surfaces as well. As applications, we give …
Quantum traces and embeddings of stated skein algebras into quantum tori
TTQ Lê, T Yu - Selecta Mathematica, 2022 - Springer
The stated skein algebra of a punctured bordered surface (or equivalently, a marked
surface) is a generalization of the well-known Kauffman bracket skein algebra of unmarked …
surface) is a generalization of the well-known Kauffman bracket skein algebra of unmarked …
Strong positivity for the skein algebras of the 4-punctured sphere and of the 1-punctured torus
P Bousseau - Communications in Mathematical Physics, 2023 - Springer
The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on
the SL 2 character variety of a topological surface. We realize the skein algebra of the 4 …
the SL 2 character variety of a topological surface. We realize the skein algebra of the 4 …
On the AJ conjecture for knots
TTQ Le, AT Tran - Indiana University Mathematics Journal, 2015 - JSTOR
We confirm the AJ conjecture [Ga2] that relates the A-polynomial and the colored Jones
polynomial for hyperbolic knots satisfying certain conditions. In particular, we show that the …
polynomial for hyperbolic knots satisfying certain conditions. In particular, we show that the …
Sliced skein algebras and geometric Kauffman bracket
The sliced skein algebra of a closed surface of genus $ g $ with $ m $ punctures,
$\fS=\Sigma_ {g, m} $, is the quotient of the Kauffman bracket skein algebra $\SxS …
$\fS=\Sigma_ {g, m} $, is the quotient of the Kauffman bracket skein algebra $\SxS …