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15 October 2019 Cluster varieties from Legendrian knots
Vivek Shende, David Treumann, Harold Williams, Eric Zaslow
Duke Math. J. 168(15): 2801-2871 (15 October 2019). DOI: 10.1215/00127094-2019-0027

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.

Citation

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Vivek Shende. David Treumann. Harold Williams. Eric Zaslow. "Cluster varieties from Legendrian knots." Duke Math. J. 168 (15) 2801 - 2871, 15 October 2019. https://doi.org/10.1215/00127094-2019-0027

Information

Received: 29 May 2017; Revised: 13 February 2019; Published: 15 October 2019
First available in Project Euclid: 26 September 2019

zbMATH: 07145322
MathSciNet: MR4017516
Digital Object Identifier: 10.1215/00127094-2019-0027

Subjects:
Primary: 53D12
Secondary: 05E99, 32S60

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 15 • 15 October 2019
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