English

Bohr-Sommerfeld profile surgeries and Disk Potentials

Symplectic Geometry 2026-05-13 v3 Geometric Topology

Abstract

We construct a new surgery type operation by switching between two exact fillings of Legendrians which we call a BSP surgery. In certain cases, this surgery can preserve monotonicity of Lagrangians. We prove a wall-crossing type formula for the change of the disk-potential under surgery with Bohr-Sommerfeld profiles. As an application, we show that Biran's circle-bundle lifts admit a Bohr-Sommerfeld type surgery. We use the wall-crossing theorem about disk-potentials to construct exotic monotone Lagrangian tori in \bPn\bP^n.

Cite

@article{arxiv.2409.11603,
  title  = {Bohr-Sommerfeld profile surgeries and Disk Potentials},
  author = {Soham Chanda},
  journal= {arXiv preprint arXiv:2409.11603},
  year   = {2026}
}

Comments

v3: Rephrased Theorem 1.4, figure added, no change in mathematical content

R2 v1 2026-06-28T18:48:27.937Z