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The Hall Algebras of Surfaces I

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.

preprint2017arXivOpen access
Benjamin CooperPeter Samuelson
math.SGmath.QA
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Benjamin CooperPeter Samuelson

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