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 submanifolds $L$, 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 $H{F}_{\ast }(H)\otimes H{F}_{\ast }(L,{\varphi }_H^1(L))\to H{F}_{\ast }(L,{\varphi }_H^1(L))$ and prove subadditivity of invariants with respect to this product.

We removed the wrong theorem from the first version, which was brought to our attention by R. Leclercq