Legendrian skein algebras and Hall algebras
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 t...
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| Format: | Journal article |
| Language: | English |
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Springer
2021
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| _version_ | 1826302892646072320 |
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| author | Haiden, F |
| author_facet | Haiden, F |
| author_sort | Haiden, F |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T05:54:20Z |
| format | Journal article |
| id | oxford-uuid:e9fd50d9-aff9-4b7e-a7db-238487ad0491 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:54:20Z |
| publishDate | 2021 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:e9fd50d9-aff9-4b7e-a7db-238487ad04912022-03-27T10:58:29ZLegendrian skein algebras and Hall algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e9fd50d9-aff9-4b7e-a7db-238487ad0491EnglishSymplectic ElementsSpringer2021Haiden, FWe 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. |
| spellingShingle | Haiden, F Legendrian skein algebras and Hall algebras |
| title | Legendrian skein algebras and Hall algebras |
| title_full | Legendrian skein algebras and Hall algebras |
| title_fullStr | Legendrian skein algebras and Hall algebras |
| title_full_unstemmed | Legendrian skein algebras and Hall algebras |
| title_short | Legendrian skein algebras and Hall algebras |
| title_sort | legendrian skein algebras and hall algebras |
| work_keys_str_mv | AT haidenf legendrianskeinalgebrasandhallalgebras |