Exotic Lagrangian tori in Grassmannians

Quantum topology

article

Marco Castronovo¹ 

[1] Columbia University

关键词: Lagrangiantori;    Grassmannians;    clusteralgebra;    Fukayacategory;    mirror symmetry;   

DOI  :  10.4171/qt/173

学科分类：内科医学

来源: European Mathematical Society

【 摘 要 】

We describe an iterative construction of Lagrangian tori in the complex Grassmannian Gr⁡(k,n)\operatorname{Gr}(k,n)Gr(k,n), based on the cluster algebra structure of the coordinate ring of a mirror Landau–Ginzburg model proposed by Marsh and Rietsch (2020). Each torus comes with a Laurent polynomial, and local systems controlled by the kkk-variables Schur polynomials at the nnn-th roots of unity. We use this data to give examples of monotone Lagrangian tori that are neither displaceable nor Hamiltonian isotopic to each other, and that support nonzero objects in different summands of the spectral decomposition of the Fukaya category over C\mathbb{C}C.

【 授权许可】

CC BY