181 citations · 551 across the 67 of their papers we have counts for
8 papers · 1 filter
Stated SL(n)-Skein Modules and Algebras
Thang T. Q. Lê, Adam S. Sikora
We develop a theory of stated SL(n)-skein modules, of 3-manifolds marked with intervals in their boundaries. They consist of linear combinations of -webs wit…
Skein algebras of surfaces
Jozef H. Przytycki, Adam S. Sikora
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 kno…
Quantizations of Character Varieties and Quantum Knot Invariants
Adam S. Sikora
Let G be a simple complex algebraic group and g its Lie algebra. We show that the g-Witten-Reshetikhin-Turaev quantum invariants determine a deformation-quantization, C_q[X_G(torus…
Confluence Theory for Graphs
Adam S. Sikora, Bruce W. Westbury
We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confl…
A categorification of the skein module of tangles
Marta M. Asaeda, Jozef H. Przytycki, Adam S. Sikora
We generalize our previous work on categorification of Kauffman bracket skein module of surfaces, by extending our homology to tangles in cylinders over surfaces, F x [0,1]. Our ho…
Categorification of the Kauffman bracket skein module of I-bundles over surfaces
Marta M. Asaeda, Jozef H. Przytycki, Adam S. Sikora
Khovanov defined graded homology groups for links L in R^3 and showed that their polynomial Euler characteristic is the Jones polynomial of L. Khovanov's construction does not exte…