Exact, graded, immersed Lagrangians and Floer theory

2014/07/15 by Garrett Alston, Alston, Garrett, Erkao Bao +1
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1407.3871

openalex publication_date 2014/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Mirror symmetry and T-duality in the complement of an anticanonical divisor

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