Comparison of spectral invariants in Lagrangian and Hamiltonian Floer theory

2014/03/25 by Jovana Đuretić, Đuretić, Jovana, Jelena Katić +3
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1403.6317

openalex publication_date 2014/03/25 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We compare spectral invariants in periodical orbits and Lagrangian Floer homology case, for closed symplectic manifold P and its closed Lagrangian submanifolds L, when ω|_π2(P,L)=0, and μ|_π2(P,L)=0. From this result, we derive a corollary considering comparison of Hofer's distance in periodic orbits and Lagrangian case. We also define a product HF_*(H)⊗ HF_*(L,ϕ¹_H(L))→ HF_*(L,ϕ¹_H(L)) and prove subadditivity of invariants with respect to this product.

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