scholarly journals Skein algebras of surfaces

2018 ◽  
Vol 371 (2) ◽  
pp. 1309-1332 ◽  
Author(s):  
Józef H. Przytycki ◽  
Adam S. Sikora
Keyword(s):  
Skein Algebras

scholarly journals Lower and Upper Bounds for Positive Bases of Skein Algebras

2020 ◽  
Author(s):  
Thang T Q Lê ◽  
Dylan P Thurston ◽  
Tao Yu
Keyword(s):  
Chebyshev Polynomials ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Positive Basis ◽  
Positive Bases ◽  
Skein Algebras

Abstract We show that 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 polynomials. For the closed torus, we show that the normalized sequence of Chebyshev polynomials of type one $(\hat{T}_n)$ is the only one that gives a positive basis.

scholarly journals Legendrian skein algebras and Hall algebras

2021 ◽  
Author(s):  
Fabian Haiden
Keyword(s):  
Product Type ◽  
Natural Homomorphism ◽  
Fukaya Category ◽  
Hall Algebra ◽  
Associative Algebras ◽  
Quantum Topology ◽  
Hall Algebras ◽  
Legendrian Links ◽  
Skein Algebras ◽  
Marked Points

AbstractWe compare two associative algebras which encode the “quantum topology” of Legendrian curves in contact threefolds of product type $$S\times {\mathbb {R}}$$ S × R . The first is the skein algebra of graded Legendrian links and the second is the Hall algebra of the Fukaya category of S. We construct a natural homomorphism from the former to the latter, which we show is an isomorphism if S is a disk with marked points and injective if S is the annulus.

scholarly journals Positive basis for surface skein algebras

2014 ◽  
Vol 111 (27) ◽  
pp. 9725-9732 ◽  
Author(s):  
Dylan Paul Thurston
Keyword(s):  
Positive Basis ◽  
Skein Algebras

scholarly journals SU(3)-skein algebras and webs on surfaces

2021 ◽  
Author(s):  
Charles Frohman ◽  
Adam S. Sikora
Keyword(s):  
Skein Algebras

scholarly journals Triangular decomposition of skein algebras

2018 ◽  
Vol 9 (3) ◽  
pp. 591-632 ◽  
Author(s):  
Thang T. Q. Lê
Keyword(s):  
Triangular Decomposition ◽  
Skein Algebras
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