Cluster varieties from legendrian knots

Vivek Shende, David Treumann, Harold Williams, Eric Zaslow

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Many interesting spaces-including all positroid strata and wild character varieties- are moduli of constructible sheaves on a surface with microsupport in a Legendrian link. We show that the existence of cluster structures on these spaces may be deduced in a uniform, systematic fashion by constructing and taking the sheaf quantizations of a set of exact Lagrangian fillings in correspondence with isotopy representatives whose front projections have crossings with alternating orientations. It follows in turn that results in cluster algebra may be used to construct and distinguish exact Lagrangian fillings of Legendrian links in the standard contact three space.

Original languageEnglish (US)
Pages (from-to)2801-2871
Number of pages71
JournalDuke Mathematical Journal
Volume168
Issue number15
DOIs
StatePublished - 2019

ASJC Scopus subject areas

  • Mathematics(all)

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