Comparison of Spectral Invariants in Lagrangian and Hamiltonian Floer Theory

Abstract

We compare spectral invariants in periodical orbits and Lagrangian Floer homology case, for closed symplectic manifold $P$ and its closed Lagrangian submanifold $L$, when $\omega|_{\pi_2(P,L)}=0$, and $\mu|_{\pi_2(P,L)}=0$. From this result, we derive a corollary considering comparison of Hofer's distance in periodic orbits and Lagrangian case. We also define a product $HF_*(H)\otimes HF_*(L,\phi^1_H(L))\to HF_*(L,\phi^1_H(L))$ and prove subadditivity of invariants with respect to this product.