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We examine three invariants for exact loops of Lagrangiansubmanifolds that are modelled on invariants introduced by LeonidPolterovich for loops of Hamiltonian symplectomorphisms. One ofthese is the minimal Hofer length in a given Hamiltonian isotopyclass. We determine the exact values of these invariants for loopsof projective Lagrangian planes. The proof uses the Gromovinvariants of an associated symplectic fibration over the 2-discwith a Lagrangian subbundle over the boundary. The last twochapters concern different topics and can be read completelyindependently.