Cluster varieties from Legendrian knots
Cluster varieties from Legendrian knots
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DOI：
10.1215/00127094-2019-0027
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发表时间：
2015-12
影响因子：
2.5
通讯作者：
V. Shende;David Treumann;H. Williams;E. Zaslow
中科院分区：
文献类型：
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作者：
V. Shende;David Treumann;H. Williams;E. Zaslow
作者：Shende，V; Treumann，D;威廉姆斯，H; Zaslow，E|摘要：© 2019杜克大学出版社。All rights reserved.许多有趣的空间，包括所有的正向层和野生字符品种，是一个表面上的勒让德链接的微支持的可构造层的模。我们表明，这些空间上的集群结构的存在可能会推导出一个统一的，系统的方式，通过构建和采取层量子化的一组确切的拉格朗日填充对应的同位素代表，其前投影有交叉交替的方向。因此，簇代数的结果可以用来构造和区分标准接触三空间中勒让德链的精确拉格朗日填充。
Author(s): Shende, V; Treumann, D; Williams, H; Zaslow, E | Abstract: © 2019 Duke University Press. All rights reserved. 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.