Legendrian skein algebras and Hall algebras

Fabian Haiden

doi:10.1007/s00208-021-02212-8

Legendrian skein algebras and Hall algebras

Fabian Haiden

University of Oxford

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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Abstract

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.

Originalsprog	Engelsk
Tidsskrift	Mathematische Annalen
Vol/bind	381
Sider (fra-til)	631-684
ISSN	0025-5831
DOI	https://doi.org/10.1007/s00208-021-02212-8
Status	Udgivet - 2021
Udgivet eksternt	Ja

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10.1007/s00208-021-02212-8Licens: CC BY

1908.10358v2Indsendt manuskript, 486 KB
Open access versionForlagets udgivne version, 1,17 MBLicens: CC BY

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Citationsformater

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AB - 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.

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Legendrian skein algebras and Hall algebras

Abstract

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