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math.GT2020
Quantum traces and embeddings of stated skein algebras into quantum tori
Thang T. Q. Lê, Tao Yu
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 surfac…
math.GT2020
Stated skein modules of marked 3-manifolds/surfaces, a survey
Thang T. Q. Lê, Tao Yu
We give a survey of some old and new results about the stated skein modules/algebras of 3-manifolds/surfaces. For generic quantum parameter, we discuss the splitting homomorphism f…
math.GT2019
Lower and Upper Bounds for Positive Bases of Skein Algebras
Thang T. Q. Lê, Dylan P. Thurston, Tao Yu
We show that the if a sequence of normalized polynomials gives rise to a positive basis of the skein algebra of a surface, then it is sandwiched between the two types of Chebyshev…