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THE HALL ALGEBRAS OF SURFACES I

Published online by Cambridge University Press:  22 October 2018

Benjamin Cooper
Affiliation:
University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, IA 52242-1419, USA ([email protected])
Peter Samuelson
Affiliation:
University of California, Riverside, Department of Mathematics, 900 University Ave., Riverside 92521, USA ([email protected])

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.

Type
Research Article
Copyright
© Cambridge University Press 2018

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