Corpus ID: 235417447

Gromov-Hausdorff distance between filtered $A_{\infty}$ categories 1: Lagrangian Floer theory

@inproceedings{Fukaya2021GromovHausdorffDB,
  title={Gromov-Hausdorff distance between filtered \$A\_\{\infty\}\$ categories 1: Lagrangian Floer theory},
  author={Kenji Fukaya},
  year={2021}
}
In this paper we introduce and study a distance, Gromov-Hausdorff distance, which measures how two filtered A $A_{\infty}$ categories are far away each other. In symplectic geometry the author associated a filtered$A_{\infty}$ category, Fukaya category, to a finite set of Lagrangian submanifolds. The Gromov-Hausdorff distance then gives a new invariant of a finite set of Lagrangian submanifolds. One can estimate it by the Hofer distance of Hamiltonian diffeomorphisms needed to send one… Expand