Exact, graded, immersed Lagrangians and Floer theory
Abstract
We develop Lagrangian Floer Theory for exact, graded, immersed Lagrangians with clean self-intersection using Seidel's setup. A positivity assumption on the index of the self intersection points is imposed to rule out certain (but not all) disc bubbles. This allows the Lagrangians to be included in the exact Fukaya category. We also study quasi-isomorphism of Lagrangians under certain exact deformations which are not Hamiltonian.
Cite
@article{arxiv.1407.3871,
title = {Exact, graded, immersed Lagrangians and Floer theory},
author = {Garrett Alston and Erkao Bao},
journal= {arXiv preprint arXiv:1407.3871},
year = {2015}
}
Comments
Streamlined exposition and added details to some proofs. Added hypothesis that the image of the Lagrangian is totally geodesic for some metric. Corrected the proof of one of the main theorems (Theorem 1.9 in this version). Weakened the statement of Theorem A.4 on asymptotic analysis. Corrected several minor errors and typos