Comparison of Spectral Invariants in Lagrangian and Hamiltonian Floer Theory

Jelena Katic, Darko Milinkovic, Jovana Djuretic


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.

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