A note on Hofer's norm

Abstract

We show that when (M,omega) is a closed, simply connected,symplectic manifold for all gamma in pi_1 (mbox{Ham}(M),id)the following inequality holds:norm{gamma}ge sup_{bar{x}}|A(bar{x})|,where norm{gamma} is the coarse Hofer's norm, bar{x} runover all extensions to D^2 of an orbit x(t)=varphi_t (z) ofa fixed point z in M, A(bar{x}) the symplectic action ofbar{x}, and the Hamiltonian diffeomorphisms {varphi_t} ofM represent gamma.