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The Hall Algebras of Surfaces I

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arxiv 1708.00889 v1 pith:5NXZ4ZUQ submitted 2017-08-02 math.SG math.QA

Benjamin Cooper , Peter Samuelson This is my paper · ORCID
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We study the derived Hall algebra of the partially wrapped Fukaya category of a surface. We give an explicit description of the Hall algebra for the disk with m marked intervals and we give a conjectural description of the Hall algebras of all surfaces with enough marked intervals. Then we use a functoriality result to show that a graded version of the HOMFLY-PT skein relation holds among certain arcs in the Hall algebras of general surfaces.

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  1. Legendrian skein algebras and Hall algebras

    math.SG 2019-08 conditional novelty 7.0 of 10

    A natural map from the graded Legendrian skein algebra of a surface to the Hall algebra of its Fukaya category is an isomorphism for disks with marked points and injective for annuli.

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