2017/03/02 by Kenji Fukaya, Fukaya, Kenji
Computer Science · Mathematics · #53D37 #53D40 #57R56 #57R58 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1703.00603
openalex publication_date 2017/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a mixture of survey article and research anouncement. We discuss Instanton Floer homology for 3 manifolds with boundary. We also discuss a categorification of the Lagrangian Floer theory using the unobstructed immersed Lagrangian correspondence as a morphism in the category of symplectic manifolds. During the year 1998-2012, those problems have been studied emphasising the ideas from analysis such as degeneration and adiabatic limit (Instanton Floer homology) and strip shrinking (Lagrangian correspondence). Recently we found that replacing those analytic approach by a combination of cobordism type argument and homological algebra, we can resolve various difficulties in the analytic approach. It thus solves various problems and also simplify many of the proofs.