2011/11/25 by Yong-Geun Oh, Yong‐Geun Oh, Oh, Yong-Geun · 1 citation
Computer Science · Mathematics · #28D10 #53D05 #53D35 #53D40 #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis #math.SG #msc:28D10 #msc:53D05 #msc:53D35 #msc:53D40
paper · pdf · doi:10.48550/arxiv.1111.5996
30http://arxiv.org/help/prep#comments pages, incorrect usage of area in the localization process is replaced by the usage of maximum principle, a coincidence theorem of local Lagrangian spectral invariants and the global ones on cotangent bundle is added; v4) exposition improved
openalex publication_date 2011/11/25 · arxiv created 2013/05/28 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Localization of Floer homology is first introduced by Floer \citefloer:fixed in the context of Hamiltonian Floer homology. The author employed the notion in the Lagrangian context for the pair (ϕH1(L),L) of compact Lagrangian submanifolds in tame symplectic manifolds (M,ω) in \citeoh:newton,oh:imrn for a compact Lagrangian submanifold L and C2-small Hamiltonian H. In this article, motivated by the study of topological Hamiltonian dynamics, we extend the localization process for any engulfable Hamiltonian path ϕH whose time-one map ϕH1 is sufficiently C0-close to the identity (and also to the case of triangle product), and prove that the value of local Lagrangian spectral invariant is the same as that of global one. Such a Hamiltonian path naturally occurs as an approximating sequence of engulfable topological Hamiltonian loop. We also apply this localization to the graphs \Graph ϕHt in (M× M, ω⊕ -ω) and localize the Hamiltonian Floer complex of such a Hamiltonian H. We expect that this study will play an important role in the study of homotopy invariance of the spectral invariants of topological Hamiltonian.