Floer Cohomology and Higher Mutations
Abstract
We extend the construction of higher mutation as introduced in Pascaleff-Tonkonog to local higher mutation, which is applicable to a larger class of monotone Lagrangians. In two-dimensional Lagrangians, local higher mutation is the same as performing a Lagrangian anti-surgery in the sense of Haug followed by a Lagrangian surgery. We prove that up to a change of local systems, the Lagrangian intersection Floer cohomology of a pair of Lagrangians is invariant under local mutation. This result generalizes the wall-crossing formula in Pascaleff-Tonkonog. For two-dimensional Lagrangians, this result agrees with the invariance result in Palmer-Woodward.
Cite
@article{arxiv.2301.08311,
title = {Floer Cohomology and Higher Mutations},
author = {Soham Chanda},
journal= {arXiv preprint arXiv:2301.08311},
year = {2024}
}
Comments
v4: Minor revisions, added an exhaustive classification result of interior disks in section 6.3, added some applications in section 7.4