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arXiv · 1708.00889

The Hall Algebras of Surfaces I

Benjamin Cooper·Peter Samuelson
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Abstract

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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Benjamin Cooper, Peter Samuelson. 2017-08-02. The Hall Algebras of Surfaces I. https://doi.org/10.1017/s1474748018000324

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