Legendrian skein algebras and Hall algebras

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We compare two associative algebras which encode the “quantum topology” of Legendrian curves in contact threefolds of product type 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.

Original languageEnglish
JournalMathematische Annalen volume
Pages (from-to)631-684
Publication statusPublished - 2021
Externally publishedYes


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