Legendrian skein algebras and Hall algebras

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